In this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow from the Limit Laws of Sequences, and

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 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 show the patterns that arise when we continuously double and take the vortex sum of numbers in the base 10 system. When doubling from 1, we get the 1248751 pattern; doubling from 3 yields

In this video, I go over modular arithmetic and show that it is essentially the same as the "vortex math" that I have been describing. Modular arithmetic is most commonly used in daily life via

In this video, I go over modular arithmetic and show that it is essentially the same as the "vortex math" that I have been describing. Modular arithmetic is most commonly used in daily life via

In this video I show that the previous result of "multiplying a number and its vortex sum yields the same vortex sum" can be written in its equivalent modulo multiplication identity. Since we

In this video I show that multiplying a number or its vortex sum (summing digits until a single digit is obtained) yields the exact same vortex sum. This is the cause of nearly all of the amazing vortex

In this video I show that multiplying a number or its vortex sum (summing digits until a single digit is obtained) yields the exact same vortex sum. This is the cause of nearly all of the amazing vortex

In this video I show that the vortex digit sum (summing the digits until we obtain 1 digit) for any base number system can be obtained quickly by using the default Base 10 Modulo function available in

In this video I show that the vortex digit sum (summing the digits until we obtain 1 digit) for any base number system can be obtained quickly by using the default Base 10 Modulo function available in

In this video I go over the modulo operation which returns the remainder of a division between two numbers. For example 100 mod 9 = 1 because 100/9 = 99 + 1/9, hence 1 is the remainder. I then prove that

In this video I show that not only is the vortex sum (summing of digits a number until 1 digit remains) is the remainder when dividing by the largest single digit, but this same number repeats indefinitely

In this video I show that not only is the vortex sum (summing of digits a number until 1 digit remains) is the remainder when dividing by the largest single digit, but this same number repeats indefinitely

In this video I show that the "vortex sum" of a number (summing up the digits until obtaining a single digit is obtained) is just the remainder when dividing the number by 9. I go over a couple

In this video I show that the "vortex sum" of a number (summing up the digits until obtaining a single digit is obtained) is just the remainder when dividing the number by 9. I go over a couple

Converting between Hexadecimal, Binary, and Decimal Number Systems In this video I go over the hexadecimal (or base sixteen) number system and show how to convert it to binary (base two) and decimal (base