 Hi and welcome to the session, I am Asha and I am going to help you with the following question that says, find the sum 2 n terms of the series whose nth term is given by n square plus 2 raised to the power n. Let's now begin with the solution and here we are given that the nth term of the series is equal to n square plus 2 raised to the power n. So let the kth term a k is equal to k square plus 2 raised to the power k and since we have to find the sum 2 n terms therefore taking summation both the sides, your summation a k k running from 1 to n is equal to summation k running from 1 to n k square plus 2 raised to the power k. This is for the equal to summation k running from 1 to n k square plus summation k running from 1 to n 2 raised to the power k this is equal to summation k square k running from 1 to n is n into n plus 1 into 2n plus 1 upon 6 plus here this is 2 raised to the power 1 plus 2 raised to the power 2 plus 2 raised to the power n. Now this is a GP series that is so on up to 2 raised to the power n and its first term is 2 and the common ratio is again 2 and the first term is a. So the sum of this GP is equal to a into r raised to the power n minus 1 upon r minus 1. So here a is 2 into 2 raised to the power n minus 1 upon 2 minus 1 which is equal to 2 times of 2 raised to the power n minus 1. Thus summation k running from 1 to n a k is equal to n into n plus 1 into 2n plus 1 upon 6 plus 2 times of 2 raised to the power n minus 1 and thus the sum up to n terms whose nth term is given as n upon 6 into n plus 1 into 2n plus 1 plus 2 times of 2 raised to the power n minus 1. So this completes the session take care and have a good day.