Q. 18

# Find the sum of the series:

In the given question we need to find the sum of the series.

For that, first, we need to find the nth term of the series so that we can use summation of the series with standard identities and get the required sum.

The series given is … to n terms.

So, nth term of the series,

By the method of partial fractions, we can factorize the above term.

On equating the like term on RHS and LHS,

2A + 2B = 0 (a)

-A + B = 1 (b)

On solving, we will get;

(1)

(2)

.

.

.

(n-1) th equation

nth equation

Now, we need to find the sum of this series, Sn.

This can be found out by adding the equation (1), (2)…up to nth term.

So, Sum of the series,

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