# Math Summation Notation

## Math Summation Notation

In mathematical formula it is indeed the addition of many number or variable which represent to give concise expression for sum of the variable as Sigma or Summation.

$\sum\limits_{i=1}^n i = \frac{n\left ( n+1 \right )}{2}$

$\sum\limits_{i=1}^n x_{i}$ This expressions shows that sum of values of x, which starting at x1 and it ending with xn .
$\sum\limits_{i=1}^n x_{i} = x_{1} + x_{2} + x_{3} +$$+ x_{n}$

$\sum\limits_{i=1}^{10} x_{i}$ This expressions shows that sum of values of x, which starting at x1 and it ending with x10 .

$\sum\limits_{i=1}^{10} x_{i} = x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} + x_{8} + x_{9} + x_{10}$

$\sum\limits_{}^{} x = x_{1} + x_{2} + x_{3} +$$+ x_{n}$

$\sum\limits_{i=1}^n x_{i}^{2} = x_{1}^{2} + x_{2}^{2} + x_{3}^{2} +$$+ x_{n}^{2}$

This expressions shows that sum the squared values of x, which starting at x1 and it ending with xn.

## Series Summation formula:

$\sum\limits_{i=1}^n i^{1} = \frac{n\cdot \left ( n+1 \right )}{2}$

$\sum\limits_{i=1}^n i^{2} = \frac{n\cdot \left ( n+1 \right )\cdot \left ( 2n+1 \right )}{6}$

$\sum\limits_{i=1}^n i^{3} = \frac{n^{2}\cdot \left ( n+1 \right )^{2}}{4}$

$\sum\limits_{i=1}^n i^{4} = \frac{n\cdot \left ( 2n+1 \right )\cdot \left ( n+1 \right )\cdot \left ( 3n^{2}+3n-1 \right )}{30}$

$\sum\limits_{i=1}^n i^{5} = \frac{n^{2}\cdot \left ( 2n^{2}+2n-1 \right )\cdot\left ( n+1 \right )^{2}}{12}$

$\sum\limits_{i=1}^n i^{6} = \frac{n\cdot \left ( 2n+1 \right )\cdot\left ( n+1 \right )\cdot \left ( 3n^{4}+6n^{3}-3n+1 \right )}{42}$

$\sum\limits_{i=1}^n i^{7} = \frac{n^{2}\cdot \left ( 3n^{4}+6n^{3}-n^{2}-4n+2 \right )\cdot \left ( n+1 \right )^{2}}{24}$

$\sum\limits_{i=1}^n i^{8} = \frac{n\cdot \left ( 2n+1 \right )\cdot \left ( n+1 \right )\cdot \left ( 5n^{6}+15n^{5}+5n^{4}-15n^{3}-n^{2}+9n-3 \right )}{90}$

$\sum\limits_{i=1}^n i^{9} = \frac{n^{2}\cdot \left ( n^{2}+n-1 \right )\cdot \left ( 2n^{4}+4n^{3}-n^{2}-3n+3 \right )\cdot \left ( n+1 \right )^{2}}{20}$

$\sum\limits_{i=1}^n i^{10} = \frac{n\cdot \left ( 2n+1 \right )\cdot \left ( n+1 \right )\cdot \left ( n^{2}+n-1 \right )\cdot \left ( 3n^{6}+9n^{5}+2n^{4}-11n^{3}+3n^{2}+10n-5 \right )}{66}$

* n = Number of terms

* i = Number sequence

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