Question

Find the sum of first n terms of each of the following series : 1 + (1 + 3) + (1 + 3 + 5) + ...

Answer 1

Answer:

Tn = [1 + (n - 1)2][3 + (n - 1)2][5 + (n - 1)2] = ( 2n - 1)(2n + 1)(2n + 3) = 8n3 + 12n2 - 2n - 3 Sn = ∑ Tn = 8∑ n3 + 12∑ n2 - 2∑ n - 3∑ 1 = 8 ...

Answer 2

Answer:

Explanation:

Sum of n odd natural numbers is n²

The given series

1+4+9+16............

Sum of squares of first n natural numbers = n(n+1)(2n+1)/6