Question

The sum to n terms of the series 1² + 2.2² + 3² + 2.4² + 5² +.................... = \(\frac {n(n + 1)^2}2\) when n is even. When n is odd, the sum is

(a) \(\frac {n^2(n + 1)}2\)

(b) \(\frac {n(n^2 - 1)}2\)

(c) n(n + 1)² (2n + 1)

(d) None of these

Answer 1

Correct option is (a) \(\frac {n^2(n + 1)}2\) 

Let n = 2k