The greatest common divisor (GCD) of two natural numbers is the largest natural number that evenly divides each.
`GCD \Large(`
`,`
`\Large)`
Pythagorean Theorem
The square of a right triangle's hypotenuse is equal to the sum of the squares of its legs.
`^2+`
`^2`
Radical Simplification
A radical symbol `(\sqrt x)` denotes the opposite of exponentiation.
If `x^n=y`, then we may equivalently write `\sqrt[n]y=x`.
Additionally, an expression like `\sqrt{4x}` may be simplified to `2\sqrt x` because
the square root can be distributed to the factors of `4` and `x`, individually.
`\Large\sqrt x`
Quadratic Formula
A quadratic equation is a polynomial of degree `2`.
The zeros of such a polynomial are given by the expression `-b\pm\sqrt{b^2-4ac}\over 2a`.
`x^2+`
`x+`
Finite Geometric Summation
A geometric series is one that has a common ratio which remains constant between terms.
The sum of a finite geometric series is `a_1(1-r^n)\over(1-r)`, where `a_1`
is the first term, `n` is the number of terms, and `r` is the common ratio.
If `r<1` and `n\to\infty`, then `r^n` approaches `0` and the formula approaches `a_1`, thereby creating the infinite sum equation
seen previously.
`\sum_{n=1}`
`*\Large(`
`{\Large)}^{n-1}`
Infinite Geometric Summation
When a geometric series has a common ratio with an absolute value of less than one, it is said to "converge".
The value to which it converges can be calculated using the formula `a_1\over(1-r)`, where `a_1` is the first term and `r` is the common ratio.