All Maths Formulas

Algebra

\sum k = 1 n k = 1 2 n (n + 1)

$\sum\limits_{k=1}^n k = \frac{1}{2}n(n+1)$

\sum k = 1 n k 2 = 1 6 n (n + 1) (2 n + 1)

$\sum\limits_{k=1}^n k^2 = \frac{1}{6}n(n+1)(2n+1)$

\sum k = 1 n k 3 = 1 4 n 2 (n + 1) 2

$\sum\limits_{k=1}^n k^3 = \frac{1}{4}n^2(n+1)^2$

1 1 - x = 1 + x + x 2 + x 3 + \dots (for - 1 < x < 1)

$\frac{1}{1-x} = 1 + x + x^2 +x^3 + \cdots \quad(\text{for } -1 < x < 1)$

1 1 + x = 1 - x + x 2 - x 3 + \dots (for - 1 < x < 1)

$\frac{1}{1+x} = 1 - x + x^2 - x^3 + \cdots \quad(\text{for } -1 < x < 1)$

e x = 1 + x + x 2 2 ! + x 3 3 ! + \dots

$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots$

ln (1 + x) = x - x 2 2 + x 3 3 - x 4 4 + \dots (for - 1 < x < 1)

$\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots \quad (\text{for } -1 < x < 1)$

sin x = x - x 3 3 ! + x 5 5 ! - x 7 7 ! + \dots

$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$

cos x = 1 - x 2 2 ! + x 4 4 ! - x 6 6 ! + \dots

$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots$

tan x = x - x 3 3 + 2 x 5 15 - 17 x 7 315 + \dots (for - π 2 < x < π 2)

$\tan\,x = x - \frac{x^3}{3} + \frac{2x^5}{15} - \frac{17x^7}{315} + \cdots \quad \left(\text{for } -\frac{\pi}{2} < x < \frac{\pi}{2} \right)$

sinh x = x + x 3 3 ! + x 5 5 ! + x 7 7 ! + \dots

$\sinh x = x + \frac{x^3}{3!} + \frac{x^5}{5!} + \frac{x^7}{7!} + \cdots$

cosh x = 1 + x 2 2 ! + x 4 4 ! + x 6 6 ! + \dots

$\cosh x = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \cdots$

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