Sum the following series to n terms:

1 + 3 + 7 + 13 + 21 + …

Solution:

Let T_n represent the nth term and let S_n represent the sum to n terms of the given series.

According to the question:

We can rewrite equation (1) as:

Upon subtracting equation (2) from (1) we get

The successive terms differ by 2, 4, 6, 8. As we can see that these differences are in A.P

Now, we have:

Therefore, the sum of the series is n/3 (n² + 2)