Find the sum of the following series upto n terms 3 × 1², 5 × 2², 7 × 3²,……..

T_n = [nth term of 3, 5, 7,….]

[nth term of 1, 2, 3,….]²

    = [3 +(n – 1)²][1 + (n – 1).1]²

    = (2n – 1) (n)²

    = n²(2n – 1) = 2n³ + n²

Hence S_n = 2∑ n³ + ∑ n²

             = 2.

             =

             =

             =