1.

The sum to n terms of the series 12 + 2.22 + 32 + 2.42 + 52 + ........ = n(n + 1)2/2 when n is even. When n is odd, the sum is(a)  n2(n + 1)/2(b)  n(n2 - 1)/2(c)  n(n+1)2 (2n+1)(d)  None of these

Answer»

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



Discussion

No Comment Found