Sequences and Series 2 Question 15

16.

The sum of the first n terms of the series 12+222+32+242+52+262+ is n(n+1)22, when n is even. When n is odd, the sum is …. .

(1988, 2M)

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Answer:

Correct Answer: 16. [n2(n+1)2]

Solution:

  1. Here, 12+222+32+242+52+ upto n terms

=n(n+1)22

[when n is even] … (i)

When n is odd, 12+222+32+242+52+n2

=12+222+32+242++2(n1)2+n2=(n1)(n)22+n2 [from Eq. (i)] =n2n12+1=n2(n+1)2

12+222+32+242+ upto n terms, when n is odd

=n2(n+1)2



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