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Question

Find the sum of n terms of the series 11.2+52.32+103.422+174.523+....

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Solution

tn=n2+1n(n+1)2n1
n2+1n(n+1)=12n+1+1n=(22n+1)(11n)
=2nn+1n1n
tn=2nnn+12n1(n1)n
tn1=2n1(n1)n2n2(n2)n1
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t2=423212
t1=2120
Sn=2nnn+1

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