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Question

Find the sum of first 10 terms of following series
S=3(1)1+5(13+23)12+22+7(13+23+33)12+22+32+....


A
440
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B
450
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C
660
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D
220
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Solution

The correct option is C 660
First we shall find the rth term of the given series

Tr=(2r+1)[r(r+1)2]2r(r+1)(2r+1)6=3r(r+1)2

Tr=32[r2+r]

Sn=Tr=32[n(n+1)(2n+1)6+n(n+1)2]

S10=32[10×11×216+10×112]

S10=32[385+55]=660

Mathematics

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