This page provides the most important formulas for summation of series of numbers.
Sum up to 'n' natural numbers
| Series | Compact | Result |
|---|---|---|
| \(1+2+3+4+...+n\) | \(\displaystyle \sum_{i=1}^n r\) | \({n(n+1) \over 2}\) |
| \(1^2+2^2+3^2+4^2+...+n^2\) | \(\displaystyle \sum_{i=1}^n r^2\) | \({n(n+1)(2n+1) \over 6}\) |
| \(1^3+2^3+3^3+4^3+...+n^3\) | \(\displaystyle \sum_{i=1}^n r^3\) | \(\lbrace {n(n+1) \over 2} \rbrace^2\) |
| \(1^4+2^4+3^4+4^4+...+n^4\) | \(\displaystyle \sum_{i=1}^n r^4\) | \({n(n+1)(2n+1)(3n^2+3n-1) \over 30}\) |
| \(1+3+5+7+...+(2n-1)\) | \(\displaystyle \sum_{i=1}^n (2r-1)\) | \({n^2}\) |
| \(2+4+6+8+...+2n\) | \(\displaystyle \sum_{i=1}^n 2r\) | \({n(n+1)}\) |
Hope you are helped with it.