Maths formulas for summation of Number Series

This page provides the most important formulas for summation of series of numbers.

Sum up to 'n' natural numbers

Series	Compact	Result
$1+2+3+4+...+n$	${\displaystyle \sum _{i=1}^{n}r}$	$\frac{n(n+1)}{2}$
$1^2+2^2+3^2+4^2+...+n^2$	${\displaystyle \sum _{i=1}^n{r}^2}$	$\frac{n(n+1)(2n+1)}{6}$
$1^3+2^3+3^3+4^3+...+n^3$	${\displaystyle \sum _{i=1}^n{r}^3}$	$\{\frac{n(n+1)}{2}{\}}^2$
$1^4+2^4+3^4+4^4+...+n^4$	${\displaystyle \sum _{i=1}^n{r}^4}$	$\frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$
$1+3+5+7+...+(2n-1)$	${\displaystyle \sum _{i=1}^n(2r-1)}$	$n^2$
$2+4+6+8+...+2n$	${\displaystyle \sum _{i=1}^{n}2r}$	$n(n+1)$

Hope you are helped with it.