If S1,S2,S3……,Sn,… are the sums of infinite geometric series who – InterviewSolution

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1.	If S1,S2,S3……,Sn,… are the sums of infinite geometric series whose first terms are 1,2,3,……n,…… and whose common ratios are 12,13,14,……1n+1…… respectively, then the value of 2n−1∑r=1S2r is
Answer» If $S_{1}, S_{2}, S_{3} \dots \dots, S_{n}, \dots$ are the sums of infinite geometric series whose first terms are $1, 2, 3, \dots \dots n, \dots \dots$ and whose common ratios are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots \dots \frac{1}{n + 1} \dots \dots$ respectively, then the value of $2 n - 1 \sum r = 1 S_{r}^{2}$ is

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