If are the sums of infinite geometric series whose first terms are and whose common ratios are respectively, n then find the values of ....

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If S_{1},S_{2},S_{3},,S_{n} are the sums of infinite geometric series whose first terms are 1,2,3,,n and whose common ratios are \frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{n + 1} respectively, then find the values of S_{1}^{2} + S_{2}^{2} + S_{3}^{3} + .. + S_{2n - 1}^{2}.: Sequence & Series (Mathematics)

S_{1},S_{2},S_{3},\ldots\ldots,S_{n}

are the sums of infinite geometric series whose first terms are

1,2,3,\ldots\ldots,n

and whose common ratios are

\frac{1}{2},\frac{1}{3},\frac{1}{4},\ldots\ldots\frac{1}{n + 1}

respectively, n then find the values of

S_{1}^{2} + S_{2}^{2} + S_{3}^{3} + \ldots\ldots.. + S_{2n - 1}^{2}