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

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

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

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,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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