<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>https://ecency.com</link><image><url>https://ecency.com/logo512.png</url><title>RSS Feed</title><link>https://ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Sun, 28 Jun 2026 22:41:10 GMT</lastBuildDate><atom:link href="https://ecency.com/created/sequences/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[Theorem 1 and the Test for the Divergence of Infinite Series]]></title><description><![CDATA[In this video, I go over Theorem 1, which states that the terms of a convergent series approach zero. Conversely, if the terms don't approach zero, the series diverges, hence providing a useful test for]]></description><link>https://ecency.com/@mes/lkt-mqv4o68i-8z4yefcd</link><guid isPermaLink="true">https://ecency.com/@mes/lkt-mqv4o68i-8z4yefcd</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Jun 2026 16:12:00 GMT</pubDate><enclosure url="https://i.ecency.com/p/2FFvzA2zeqoVJ2SVhCmHM3NE9RmdFMdJFE9fqEwGLZPjJDBujuMaY1roNVRzaS9iMMDHEd5djEysEUb7RudgA95mEUxmgqPGSZJADUJ27duUGfQbgQeKDdZV5Ye8F?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Telescoping Sum: All the terms of this series cancel out except for the first and last term]]></title><description><![CDATA[In this video, I go over an infinite series in which arises an example of the famous telescoping sum such that all the terms of the series cancel except for the first and last term. The telescoping sum]]></description><link>https://ecency.com/@mes/lkt-mqncu4tw-rlviqoqk</link><guid isPermaLink="true">https://ecency.com/@mes/lkt-mqncu4tw-rlviqoqk</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 21 Jun 2026 05:38:21 GMT</pubDate><enclosure url="https://i.ecency.com/p/2FFvzA2zeqoVJ2SVhCmHM3NE9RmdFMdJFE9fqEwGLZPjJDBujuMaY1rnwqU9isHm2hXifR99ENp5drhBjNcWAt21X6BY1sgx43A6p1NuQ8jSdTYYEpAB3uBKAuB83?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Geometric Series: Sum of x^n series = 1/(1 - x) if |x| is less than 1]]></title><description><![CDATA[In this video, I show that the infinite series xn = x0 + x1 + x2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x0 = 1, so the first term]]></description><link>https://ecency.com/@mes/lkt-mqkhywq8-4pz1cse0</link><guid isPermaLink="true">https://ecency.com/@mes/lkt-mqkhywq8-4pz1cse0</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 19 Jun 2026 05:38:33 GMT</pubDate><enclosure url="https://i.ecency.com/p/3W72119s5BjVs3Hydympjx5SWPMR58VM5G7WSBzEKEVhf4AYkK1TYHTGU3ozeqeTxVDEWUyPwMrmfk2h1UUsEmTZRXDPPDnrJzcqwX5n9mFG9GVwMjvRPm?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Converting the number 2.3171717... into the fraction 1147/495 via the Geometric Series]]></title><description><![CDATA[In this video, I go over an example of converting the number 2.3171717... (with infinite repeating 17) into a fraction by writing the repeating 17s as an infinite geometric series with common ratio 1/100,]]></description><link>https://ecency.com/@mes/lkt-mqho00lr-zb7aqbc0</link><guid isPermaLink="true">https://ecency.com/@mes/lkt-mqho00lr-zb7aqbc0</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 17 Jun 2026 06:04:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/2r8F9rTBenJQfQgENeTSahwbgwXbiWivavXVxnXvHWdq1EHJJvCdc95vihqj2KJLY52woXg7EPWSWgCrWDBRAg2coDs6wh8cqZmhUDhGFgrp3v3u6hd9f2uvBxDhnqdM9?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Examples on Identifying Geometric Series and Determining if it Converges or Diverges]]></title><description><![CDATA[In this video, I go over two examples and two methods of identifying if a series is a geometric series, and then finding its sum if it converges. In the first example, we are given the first 4 terms of]]></description><link>https://ecency.com/@mes/lkt-mqfihsb2-ll6acz8a</link><guid isPermaLink="true">https://ecency.com/@mes/lkt-mqfihsb2-ll6acz8a</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 15 Jun 2026 17:54:39 GMT</pubDate><enclosure url="https://i.ecency.com/p/JvFFVmatwWHRfvmtcpYX4AcBBJcJkutBQvuCLHCkKuezzPjpFaARXZV164wYnPX43smCfpA3f9C7F11R4wPDf7os4MfVGhozZjvr7uBcqdXbxeFr6BSiqbvo4MNEVjEqag4qXKM71R?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Geometric Series: Deriving the Sum using an Ingenious Method (and via Similar Triangles)]]></title><description><![CDATA[In this video, I go over the geometric series, which is the sum a + a r + a r^2 + ..., and show that if the absolute value of the common ratio r is less than 1, then the sum is just the first term divided]]></description><link>https://ecency.com/@mes/lkt-mqaiqkog-mbkxv9l6</link><guid isPermaLink="true">https://ecency.com/@mes/lkt-mqaiqkog-mbkxv9l6</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 12 Jun 2026 06:02:24 GMT</pubDate><enclosure url="https://i.ecency.com/p/6VvuHGsoU2QBt9MXeSvT9TSh2CKxzN3D7o3GPvWWhKyKgxo9nN5q1tnigNVq5q3H6ByDP57TirD9tBxwR7aB8Jew4WGCPYNkF6B1LNvq1oiLeznqNmZCt3CGo8KJ4X?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition and Notation of Infinite Series]]></title><description><![CDATA[In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite sequence of numbers whose terms are each]]></description><link>https://ecency.com/@mes/definition-and-notation-of-infinite-series</link><guid isPermaLink="true">https://ecency.com/@mes/definition-and-notation-of-infinite-series</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 10 May 2026 05:57:39 GMT</pubDate><enclosure url="https://i.ecency.com/p/8th8uW8KLF3eHoH9cP9Etf4AqMgNKtKoyu4fqZraWgFsdvwTnXiBR7fX6qjTwUSDaij4GrBFn2GxHTSBernYYQkUVwy3myojj65NV9XN2yXZC6Ni9dGY4Z67xeJr8FGr1W9W6Hc4B85gPTCEt2JJRj4qX2SLbYZbsfGGYenoMZ5q5EyiW94Ee6efYT?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition and Notation of Infinite Series]]></title><description><![CDATA[In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite sequence of numbers whose terms are each]]></description><link>https://ecency.com/@mes/2957acdd</link><guid isPermaLink="true">https://ecency.com/@mes/2957acdd</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 10 May 2026 05:30:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhvVb4hMXdUrtadSx9oHTypxd7hGM1MQ9beyqMoGR6jLK?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[History of the Fibonacci Sequence and the Golden Ratio]]></title><description><![CDATA[In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. - summary - playlist - notes #math]]></description><link>https://ecency.com/@mes/history-of-the-fibonacci-sequence-and-the-golden-ratio</link><guid isPermaLink="true">https://ecency.com/@mes/history-of-the-fibonacci-sequence-and-the-golden-ratio</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 23 Apr 2025 15:34:57 GMT</pubDate><enclosure url="https://i.ecency.com/p/3ejZQFLqXedKXKhURdjx14Sr8NSYZmTdw2HQuQXkeUsn4X1LM6CBB67BuRZfi9A2ZNtn9uArKeq9WKBQ47Y4CC9QALpHczaojwc8MsBxX1XkDxpCr6FBKvNGw2VzJwQ4YRBxk2ThYa3kHKuToGJfsfLq17tJzqBHs6kWh7VNHpAk1YyfYMEsgJEs7N2Ru?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[History of the Fibonacci Sequence and the Golden Ratio]]></title><description><![CDATA[In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. Although the Fibonacci sequence]]></description><link>https://ecency.com/@mes/mhaunidd</link><guid isPermaLink="true">https://ecency.com/@mes/mhaunidd</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 23 Apr 2025 05:33:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVhdYcAAo5zoENoGD91i2S2SrpCcqpT7Mw4xjoapLKpkmDinBQKhnPdyjtbvT6559ZNCcA5WbQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio)]]></title><description><![CDATA[In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo]]></description><link>https://ecency.com/@mes/exercise-4-fibonaccis-original-rabbit-reproduction-sequence-and-the-golden-ratio</link><guid isPermaLink="true">https://ecency.com/@mes/exercise-4-fibonaccis-original-rabbit-reproduction-sequence-and-the-golden-ratio</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sat, 19 Apr 2025 03:53:42 GMT</pubDate><enclosure url="https://i.ecency.com/p/6pu4ZRycQdDVScudzYNpYELDa4hYsxmKLHRL1gYdYaPsV2FdPGpnanPFaYJYH8XCtUgpDQfB1Ecowq8HtmojudMkHbYwkogP8r35PKz5yA4VqabGfSdES6xzRCTgpF5azxNJDyUu7fWHvkwa6aXpc5263xKVd5hQiVyW7nQyMZjKUNju6sax7vixKz27bh1SzCjaf?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio)]]></title><description><![CDATA[In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo]]></description><link>https://ecency.com/@mes/neiphblh</link><guid isPermaLink="true">https://ecency.com/@mes/neiphblh</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 18 Apr 2025 19:14:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVcMwEmp4kfqXNebygsdky8UQQcSjLfKzJStNnboR59fCTsHG3ydzo4dVVAaSsGx7Cv6QY5xfg?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 3: Convergent Sequence inside a Continuous Function]]></title><description><![CDATA[In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). - summary - playlist - notes #math #sequences]]></description><link>https://ecency.com/@mes/exercise-3-convergent-sequence-inside-a-continuous-function</link><guid isPermaLink="true">https://ecency.com/@mes/exercise-3-convergent-sequence-inside-a-continuous-function</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 16 Apr 2025 03:25:36 GMT</pubDate><enclosure url="https://i.ecency.com/p/YpihifdXP4WMLzfwe2d1rg9TCZREQLPRYL4YgsSppLMNpvS2ixKzPv8Gknh4UJ8BUSqSN1WkkbS1GjQDsU9uxJmtkW1UZ9UgwAwvaTkyjnvPhGowYqZG6bcQPEHJPtUqgqf52XhrZJVHhGdE93gAjrNWPae6yLKFhZN4QuDn7L5V?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 3: Convergent Sequence inside a Continuous Function]]></title><description><![CDATA[In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). I prove this using the precise definition]]></description><link>https://ecency.com/@mes/mfhyczas</link><guid isPermaLink="true">https://ecency.com/@mes/mfhyczas</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 16 Apr 2025 03:00:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxKVScqqVB6h4EZ5KQyM4pRLaH9bSzkh8gky3LQDh85khF4kbamSwxqNaUtLFRCWPdSfTjZC2?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 2: If the limit of the absolute values of a sequence is zero, so is the sequence]]></title><description><![CDATA[In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the]]></description><link>https://ecency.com/@mes/exercise-2-if-the-limit-of-the-absolute-values-of-a-sequence-is-zero-so-is-the-sequence</link><guid isPermaLink="true">https://ecency.com/@mes/exercise-2-if-the-limit-of-the-absolute-values-of-a-sequence-is-zero-so-is-the-sequence</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 17:40:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/YpihifdXP4WMLzfwe2d1rg9TCZREQLPRYL4YgsSppLMNpvS2ixKzPv8FPStnzawaxvbNC8Vzwpiw54H5wssaRrM7yMgS9cwQ9dq454XnbT95h2ErDmbmdijCh1eSJziVw3LyFdzvgvEwGxAhZPJ3YGcW33tVZFqx2ETFHRYaT7AF?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 2: If the limit of the absolute values of a sequence is zero, so is the sequence]]></title><description><![CDATA[In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the]]></description><link>https://ecency.com/@mes/sgnogped</link><guid isPermaLink="true">https://ecency.com/@mes/sgnogped</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 16:46:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxKxJkNCNjFvGmgBX47GJP4f3NEM6be81vUQrPiCtMdMJM3zJ2ytBegnEApeVy3UTjjM3rTtr?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 1: Limit of a Sequence and the Golden Ratio (Minus 1)]]></title><description><![CDATA[In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence by plugging in the limit into the recursion]]></description><link>https://ecency.com/@mes/exercise-1-limit-of-a-sequence-and-the-golden-ratio-minus-1</link><guid isPermaLink="true">https://ecency.com/@mes/exercise-1-limit-of-a-sequence-and-the-golden-ratio-minus-1</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 04:58:18 GMT</pubDate><enclosure url="https://i.ecency.com/p/4bEjbgCbFMvA8T33kGvF6kHce4BTcm88Pv5WXm8EBoMz3u29V4LrZvMEwg8eVJ9osbigz59aF5YU4hgWFyaRurY5BxjCBBUNehsYsAE59jkA3wZkYSg4GoY3TzvM3mzLQA6Ywd4dtb6xNgoaFKKg9KMH6fKzwGBRPhGmXAFkwuntYMkG8f?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 1: Limit of a Sequence and the Golden Ratio (Minus 1)]]></title><description><![CDATA[In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence by plugging in the limit into the recursion]]></description><link>https://ecency.com/@mes/verunqmp</link><guid isPermaLink="true">https://ecency.com/@mes/verunqmp</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 04:29:09 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVvUQxoZpqYt9uEyQpYT1AoKFhzdSqQTdStgC3PTPZjLBXGG6YtXoqybE3fABXdWzs1TVmbVhY?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Bounded Sequences, Completeness Axiom, and the Monotonic Sequence Theorem]]></title><description><![CDATA[In this video I first go over the definition of bounded sequences, then discuss the completeness axiom in number theory and how it is used to proof the monotonic sequence theorem. - summary - playlist]]></description><link>https://ecency.com/@mes/bounded-sequences-completeness-axiom-and-the-monotonic-sequence-theorem</link><guid isPermaLink="true">https://ecency.com/@mes/bounded-sequences-completeness-axiom-and-the-monotonic-sequence-theorem</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 11 Apr 2025 17:34:45 GMT</pubDate><enclosure url="https://i.ecency.com/p/2Snpznz7rwiEdJnR5Rzb8HdpDtLFUR7vWRCLde6bYWedt2juHpQ1aLpvzjdaZjnhg33xgd2Qbgs4KEicAXCXPZ9Spk4KeHevX2H3mfPCtgHC31S1CUmhDcrkwhezmCeobm4y1i5eBwUb5H99DuzjGZ4TUWqFcjN7YRCXUysDM1NbDfmPy4UccmDa7QQdbDGS22G78vMEQwwSw1KyjfD?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Bounded Sequences, Completeness Axiom, and the Monotonic Sequence Theorem]]></title><description><![CDATA[In this video I first go over the definition of bounded sequences, then discuss the completeness axiom in number theory and how it is used to proof the monotonic sequence theorem. A sequence is bounded]]></description><link>https://ecency.com/@mes/msxghnik</link><guid isPermaLink="true">https://ecency.com/@mes/msxghnik</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 11 Apr 2025 17:11:06 GMT</pubDate><enclosure url="https://i.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxbZQBgpagBNwKBEab89zWKKfnqrSinwaLRmHdnfKw8jTCJf6b7W5crkki2bYxtvsNWd2Koev?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>