 Hi and welcome to the session. I am Asha and let us solve the following question which says find the sum 2 n terms of the series 3 into minus square plus 5 into 2 square plus 7 into 3 square plus so on. So, let us start with the solution and let the given series be denoted by s. So, here s is equal to 3 into 1 square plus 5 into 2 square plus 7 into 3 square plus so on and let the kth term of the series be ak. The ak will be equal to 2k plus 1 into k square since the first term can be written as 2 into 1 plus 1 into 1 square. So, here the first term k is equal to 1 and the second term k will be 2 since 2 into 2 plus 1 is 5 into 2 square plus 2 into 3 plus 1 into 3 square thus the nth term will be 2n plus 1 into n square. Now, we have to find the sum up to n terms. Therefore, taking summation on both the sides k running from 1 to n we have k plus 1 into k square which is further equal to summation k running from 1 to n 2k cube plus k square or it is further written as 2 times summation k cube k running from 1 to n plus summation k running from 1 to n k square or equal to 2 into summation k cube k running from 1 to n as n square into n plus 1 whole square or 4 plus summation k running from 1 to n k square is n into n plus 1 into 2n plus 1 upon 6. This is further equal to n square into n plus 1 whole square upon 2 plus n into n plus 1 into 2n plus 1 upon 6 or it is further written as taking n and n plus 1 upon 6 common we have 3 times n into n plus 1 plus 2n plus 1 or n into n plus 1 upon 6 3n square plus 3n plus 1 which is further equal to n into n plus 1 upon 6 into 3n square plus 5n plus 1 and that is the answer is 3 into 1 square plus 5 into 2 square plus 7 into 3 square plus up to n term which is 2n plus 1 into n square is equal to n upon 6 into n plus 1 into 3n square plus 5n plus 1. So, this completes the session. Take care and have a good day.