A series indicates the summation of a given function. According to the number of terms the summation is different. Using this formula one can calculate the summation of different functions. The **series formula** is given as,

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Let us discuss the solved problems of different series.

### Solved Examples

**Question 1: **Find out $\sum_{i=1}^{4}x^{2}$+2 ?

** Solution: **

Given series is,

$\sum_{i=1}^{4}$ $x^{2}$+2

Expanding this series,

(1^{2}) + 2 = 3

(2^{2}) + 2 = 6

(3^{2}) + 2 = 11

(4^{2}) + 2 = 18

So, $\sum_{i=1}^{4}$ $x^{2}$+2 = 3+6+11+18 = 38

**Question 2: **Evaluate $\sum_{i=1}^{5}$x+2 ?

** Solution: **

Given series is,

$\sum_{i=1}^{5}$ x+2

The expansion is,

1 + 2 = 3

2 + 2 = 4

3 + 2 = 5

4 + 2 = 6

5 + 2 = 7

So, $\sum_{i=1}^{5}$ x+2 = 3 + 4 + 5 + 6 + 7 = 25

Given series is,

$\sum_{i=1}^{4}$ $x^{2}$+2

Expanding this series,

(1

(2

(3

(4

So, $\sum_{i=1}^{4}$ $x^{2}$+2 = 3+6+11+18 = 38

Given series is,

$\sum_{i=1}^{5}$ x+2

The expansion is,

1 + 2 = 3

2 + 2 = 4

3 + 2 = 5

4 + 2 = 6

5 + 2 = 7

So, $\sum_{i=1}^{5}$ x+2 = 3 + 4 + 5 + 6 + 7 = 25

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