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Question

The sum of the series 131+13+231+3+13+23+331+3+5+ upto 16 terms is

A
246
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B
646
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C
446
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D
746
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Solution

The correct option is C 446
Given : 131+13+231+3+13+23+331+3+5+
Now,
Tn=nr=1r3nr=1(2r1)Tn=14×n2(n+1)22(n(n+1)2)nTn=14(n+1)2S16=14(22+32+42+172)S16=14(12+22+32+42+17212)S16=14(17(17+1)(217+1)61)S16=446

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