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

Tinku Tara June 4, 2023 Limits 0 Comments

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

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

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{S}_{\mathrm{1}} {S}_{{n}} +{S}_{\mathrm{2}} {S}_{{n}−\mathrm{1}} +{S}_{\mathrm{3}} {S}_{{n}−\mathrm{2}} +…+{S}_{{n}} {S}_{\mathrm{1}} }{{S}_{\mathrm{1}} ^{\mathrm{2}} +{S}_{\mathrm{2}} ^{\mathrm{2}} +…+{S}_{{n}} ^{\mathrm{2}} } \\ $$$${when}\:{S}_{{n}} \:{is}\:{sum}\:{of}\:{infinite}\:{series}\:{whose} \\ $$$${first}\:{term}={n}\:\:\:{and}\:{common}\:{ratio}\:\frac{\mathrm{1}}{{n}+\mathrm{1}} \\ $$$${find}\:{the}\:{value}\:{of}\:{limit} \\ $$

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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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