algebra Tag Posts Index

Theorem 2: Series of Sums is equal to Sum of Series

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

Theorem 1 and the Test for the Divergence of Infinite Series

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,

Telescoping Sum: All the terms of this series cancel out except for the first and last term

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

Geometric Series: Sum of x^n series = 1/(1 - x) if |x| is less than 1

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

Converting the number 2.3171717... into the fraction 1147/495 via the Geometric Series

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: Deriving the Sum using an Ingenious Method (and via Similar Triangles)

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,

Vortex Math Doubling Patterns: 1248751, 3636, 9999

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

Vortex Math is Based on the Modulo Multiplication Identity

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

Modular Arithmetic = Vortex Math

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

Vortex Math is Based on the Modulo Multiplication Identity

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

Multiplying a Number and Its Vortex Sum Results in the Same Vortex Sum

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

Multiplying a Number and Its Vortex Sum Results in the Same Vortex Sum

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

Using Base 10 to Calculate Vortex Sum of Different Number Systems

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

Using Base 10 to Calculate Vortex Sum of Different Number Systems

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

Modulo Operation – Vortex Digit Sum is Equal to the Mod (base - 1)

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

Vortex Math: Summing Digits of a Number is the Remainder AND Repeating Digit of Division

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,

Vortex Math: Summing Digits of a Number is the Remainder AND Repeating Digit of Division

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,

Vortex Math: Summing the Digits of a Number is just the Remainder

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

Vortex Math: Summing the Digits of a Number is just the Remainder

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

Converting between Hexadecimal, Binary, and Decimal Number Systems

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