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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}} }…
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