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Series Calculator
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Series is the word generally used to denote number of things, events or anything taken together. Here in maths it is used to find the sum of first n natural numbers for any expression have n terms.

Series Calculator calculates the value of sum of any expression of n natural numbers.

You can see a default function with its range given below. The calculator will find the value of the function by solving the function with respect to its range and adding up those values when u click on "Calculate".

## Steps for Series Calculator

Step 1 :

Read the function and observe the range given.

Step 2 :

Solve the given function particularly for all the values. Add all these Values to get the answer.

## Problems on Series Calculator

1. ### Solve : $\sum_{1}^{5}$ (2n2 + 1)

Step 1 :

given function is $\sum_{1}^{5}$ (2n2 + 1) and the range given is {1,2,3,4,5}.

Step 2 :

Since range is {1,2,3,4,5}

For n = 1, (2n2 + 1) = 2(1)2 + 1 = 3

For n = 2, (2n2 + 1) = 2(2)2 + 1 = 9

For n = 3, (2n2 + 1) = 2(3)2 + 1 = 19

For n = 4, (2n2 + 1) = 2(4)2 + 1 = 33

For n = 5, (2n2 + 1) = 2(5)2 + 1 = 51.

The series for given function $\sum_{1}^{5}$ (2n2 + 1) = 3 + 9 + 19 + 33 + 51 = 115.

$\therefore$ $\sum_{1}^{5}$ (2n2 + 1) = 115.

2. ### $\sum_{1}^{3}$ (n-2 + 1)

Step 1 :

Given function is $\sum_{1}^{5}$ (2n2 + 1) and the range given is {1,2,3}.

Step 2 :

Since range is {1,2,3}

For n = 1, (n-2 + 1) = (1)-2 + 1 = 1 +1 = 2

For n = 2, (n-2 + 1) = (2)-2 + 1 = $\frac{1}{4}$ + 1 = $\frac{5}{4}$

For n = 3, (n-2 + 1) = (3)-2 + 1 = $\frac{1}{9}$ + 1 = $\frac{10}{9}$

The series for given function $\sum_{1}^{3}$ (n-2 + 1) = 2 + $\frac{5}{4}$ + $\frac{10}{9}$

= $\frac{72 + 45 + 40 }{36}$

$\therefore$ $\sum_{1}^{3}$ (n-2 + 1) = $\frac{157}{36}$.