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Question

Sum of n terms of the following series 12+33+53+73+ is

A
n2(2n21)
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B
n3(n1)
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C
n3+8n+4
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D
2n4+3n2
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Solution

The correct option is A n2(2n21)
The nth term of given series tn=(2n1)3
Sum of series =tn=(2n1)3
{(8n33.4n2+3.2n1)}
=2n2(n+1)22n(n+1)(2n+1)+3n(n+1)n
=2n4+4n3+2n22n[2n2+3n+1]+3n2+3nn
=2n4+4n3+2n24n36n22n+3n2+3nn
=2n4n2
=n2(2n21)

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