If S1,S2,S3⋯Sp are the sums of infinite geometric series whose first terms are 1,2,3,... p and whose common ratios are 12,13,14,⋯1p+1respectively, Then S1+S2+S3+⋯+Sp=
A
p(p+1)2
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B
p(p+3)2
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C
p
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D
None of these
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Solution
The correct option is Bp(p+3)2 S1=a1−r=11−12=2,S2=21−13=223=3,S3=31−14=334=4SP=p1−1p+1ppp+1=p+1∴S1+S2+S3+⋯+Sp=p2(2+p+1)=p(p+3)2