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

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} + \dots + S_{n} S_{1}}{S_{1}^{2} + S_{2}^{2} + \dots + 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