Math Formulas || Series Formulas || Finite Series

$\sum\limits_{k=1}^n k = \dfrac{1}{2} ~ n(n+1)$
$\sum\limits_{k=1}^n 2k ={n(n+1)}$
$\sum\limits_{k=0}^{n-1} 2k+1 ={n^2}$
$\text{k} \enspace + \enspace \text{k+1} \enspace + \enspace \text{k+2} + \cdots + \text{k+n-1}$ $=\dfrac{n(2k+n-1)}{2} $
$\sum\limits_{k=1}^n k^2 = \dfrac{1}{6}~n(n+1)(2n+1)$
$\sum\limits_{k=1}^n k^3 = \dfrac{1}{4}~n^2(n+1)^2$
$\sum\limits_{k=0}^{2n-1} k^2 = \dfrac{n(4n^2-1)}{3}$
$\sum\limits_{k=0}^{2n-1} k^3 = {n^2(2n^2-1)}$
$1 + \dfrac{1}{2} + \dfrac{1}{4} +\dfrac{1}{8} + \cdots \dfrac{1}{2^n}=2$
$\dfrac{1}{1 \cdot 2} + \dfrac{1}{2 \cdot 3} + \dfrac{1}{3 \cdot 4} + \cdots \dfrac{1}{1 \cdot n(n+1)}$ $=1$
$1 + \dfrac{1}{1!} + \dfrac{1}{2!} +\dfrac{1}{3!} + \cdots \dfrac{1}{(n-1)!}=e$