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Category: Limits

Question-189382

Question Number 189382 by TUN last updated on 15/Mar/23 Answered by Ar Brandon last updated on 15/Mar/23 Useintegrationbypartswith;a.u(x)=x3+1andv(x)=e3x2$${b}.\:\mathrm{u}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −{x}+\mathrm{2}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{{x}−\mathrm{2}} \

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 $$\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}} }…