Correct option (a) n2(n + 1)/2
Explanation:
12 + 2.22 + 32 + 2.42 + 52 + ........ + (2k - 1)2 + 2(2k)2
= 2k(2k + 1)2/2
Let n = 2k + 1 (odd)
12 + 2.22 + 32 + 2.42 + 52 + ........ + (2k - 1)2 + 2(2k)2 + (2k + 1)2
= 2k(2k + 1)2 /2 + (2k + 1)2
= (2k + 1)2 (2k + 2)/2 = n2(n + 1)/2