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

For that, first, we need to find the n^th 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, n^th 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

→ n^th equation

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

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

So, Sum of the series,