Summation is something which calculate the sum value by adding the given sequence for each value of the given interval. It is denoted by $\sum$.

If S is the given sequence, then Summation formula is given by Summation Calculator also known as Sigma Notation Calculator (Sigma Calculator) is a online tool to calculate the sum of the series. Provided are the three blocks where you are supposed to enter the sequence given, starting and end point of the given interval.

## How to Calculate Summation

Steps for solving the summation

Step 1 :
Read the given problem and observe the series and the intervals given

Step 2 : Use summation formula

$\sum_{n = 1}^{k}$ $S$ = $S_{1} + S_{2} + S_{3} + ..... + S_{k}$

Here $S$ is given sequence. Substitute the values of the each interval in the sequence and adding all the interval values of sequence to get the answer.

Below are some Examples based on summation which may be helpful for you.

### Solved Examples

Question 1: Evaluate: $\sum_{x=1}^{4}$ ($\frac{1}{x+1}$)
Solution:

Step 1: The given sequence is $\sum_{x=1}^{4}$ $\frac{1}{x+1}$

Step 2: $\sum_{x=1}^{4}$ $\frac{1}{x+1}$ = $\frac{1}{1+1}$ + $\frac{1}{2+1}$ + $\frac{1}{3+1}$ + $\frac{1}{4+1}$

= $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{1}{5}$

= $\frac{77}{60}$

= 1.28.

Question 2: Evaluate: $\sum_{x=0}^{5}$ (x2 + 1)
Solution:

Step 1: The given sequence is $\sum_{x=0}^{5}$ (x2 + 1)

Step 2: $\sum_{x=0}^{5}$ (x2 + 1) = (02 + 1) + (12 + 1) + (22 + 1) + (32 + 1) + (42 + 1) + (52 + 1)

= 1 + 2 + 5 + 10 + 17 + 26 = 61.

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