# SUMMATION FORMULA

When large number of data are concerned, then summation is needed quite often. To write a very large number, summation notation is useful.  The sequence [1,2,4,2..] whose value is the sum of the each number in the sequence is summation. In simple words, summation notation helps write a short form for addition of very large number of data. We use this symbol –

We use this symbol –  , called sigma to denote summation. When a sequence is needed to add from left to right, it could run intermediate result in a partial sum, running total or prefix sum.

The form in which the summation notation is used:

$\large x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+……..x_{n}=\sum_{i-n}^{n}x_{i}$

To make it clear, read what each notation in the summation formula stands for:

This expression is read as “The sum of x sub i from i equals 1 to n”.

### Solved Example

Question: Evaluate: $\sum_{x-0}^{4}x^{4}$

The expression can be written as:

$\sum_{x-0}^{4}x^{4}=\left(0\right)^{2}+\left(1\right)^{2}+\left(2\right)^{2}+\left(3\right)^{2}+\left(4\right)^{2}$

$=0+1+16+81+256=354$