IIT JEE past question AP GP 5

S1, S2, S3.... Sn are sums of infinite Geometric series whose first terms are 1,2,3,....n and common ratios are 1/2, 1/3... 1/n+1 respectively

then

S1²+S2²+S3.... +Sn²=?

4 Answers

for
S₁ a=1 and r = 1/2
S₁ = a/1-r
thus
S₁= 1/1-1/2 = 2
similarly
S₂= 3

S1²+S2²+S^3.... +Sn²
= 2²+3²+4²+...+n²
= n(n+1)(2n+1)/6-1
= n(n+1)(2n+1)-6/6

anirudh check more closely

is this sum uptil n^2 or (n+1)^2?>

yes sir. it will be upto (n+1)² .

so the ans should be

(n+1)(n+2)(2n+3)-6/6

i hope now it is correct?

yup anirudh...

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