 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 two n terms of each of the following series. First is 1 into 2 plus 2 into 3 plus 3 into 4 plus 4 into 5 plus so on. Let us now begin with the solution and let the k term of the given series be denoted by ak. So the general term ak would be equal to k into k plus 1 since the first term can be written as 1 into 1 plus 1, second term can be written as 2 into 2 plus 1, third term can be written as 3 into 3 plus 1, fourth term can be written as 4 into 4 plus 1 and so on. And now since we need to find the sum two n terms therefore taking summation on both the sides, k running from 1 to n ak is equal to summation k square plus k, k running from 1 to n. This is further equal to summation k running from 1 to n k square plus summation k running from 1 to n k. Now summation k square such that k running from 1 to n is equal to n into n plus 1 into 2n plus 1 upon 6 plus and summation k, k running from 1 to n is n into n plus 1 upon 2. But in further simplifying comes equal to n into n plus 1 upon 6 to n plus 1 plus 3. So this is equal to n into n plus 1 upon 6 into 2 times of n plus 2. So 2, 3s are 6 and the answer is n into n plus 1 into n plus 2 upon 3. And therefore the answer is 1 into 2 plus 2 into 3 plus 3 into 4 plus 4 into 5 plus so on up to n into n plus 1 is equal to n into n plus 1 into n plus 2 upon 3 into n plus 1 into n plus 2. So this concludes the session. Take care and have a good day.