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Question

The sum of n terms of the series 22+42+62+....is


A

n(n+1)(2n+1)6

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B

2n(n+1)(2n+1)3

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C

n(n+1)(2n+1)3

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D

none of these

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Solution

The correct option is B

2n(n+1)(2n+1)3


Explanation for the correct option:

Find the required sum.

Given: series 22+42+62+....nterms

Here tn=(2n)2

=4n2

Sum, S=4n2

=4n2=4n(n+1)(2n+1)6=2n(n+1)(2n+1)3

Therefore, the sum of n terms of the series 22+42+62+....is 2n(n+1)(2n+1)3.

Hence option (B) is the correct answer.


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