lim_(n→∞) ((S_1 S_n +S_2 S_(n−1) +S_3 S_(n−2) +...+S_n S_1 )/(S_1 ^2 +S_2 ^2 +...+S_n ^2 )) when S_n is sum of infinite series whose first term=n and common ratio (1/(n+1)) find the value of limit


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Question Number 58247 by tanmay last updated on 20/Apr/19

$\lim_{n \to \infty} \frac{S_{1} S_{n} + S_{2} S_{n - 1} + S_{3} S_{n - 2} + . . . + S_{n} S_{1}}{S_{1}^{2} + S_{2}^{2} + . . . + S_{n}^{2}}$ $w h e n S_{n} i s s u m o f i n f i n i t e s e r i e s w h o s e$ $f i r s t t e r m = n a n d c o m m o n r a t i o \frac{1}{n + 1}$ $f i n d t h e v a l u e o f l i m i t$
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