let-t-0-and-f-t-t-1-t-prove-that-the-sequence-S-n-k-1-n-f-k-n-2-converges-and-find-its-limit-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 32335 by abdo imad last updated on 23/Mar/18

let t≥0 and f(t) =(t/( (√(1+t)))) .prove that the sequence S_n = Σ_(k=1) ^n f((k/n^2 )) converges and find its limit.

$${let}\:{t}\geqslant\mathrm{0}\:{and}\:{f}\left({t}\right)\:=\frac{{t}}{\:\sqrt{\mathrm{1}+{t}}}\:.{prove}\:{that}\:{the}\:{sequence} \\ $$$${S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:{converges}\:{and}\:{find}\:{its}\:{limit}. \\ $$

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let-t-0-and-f-t-t-1-t-prove-that-the-sequence-S-n-k-1-n-f-k-n-2-converges-and-find-its-limit-

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