If \(S_{1},S_{2},S_{3},\ldots\ldots,S_{n}\) 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,\\ then find the values of \(S_{1}^{2} + S_{2}^{2} + S_{3}^{3} + \ldots\ldots.. + S_{2n - 1}^{2}\). - Math Practice Question | divineJEE