Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 32303 by abdo imad last updated on 22/Mar/18

find lim_(n→∞) Σ_(k=1) ^n (1/(2n+k)) .

findlimn→∞∑k=1n12n+k.

Commented by abdo imad last updated on 01/Apr/18

let put S_n = Σ_(k=1) ^n (1/(2n+k)) S_(n ) =(1/n) Σ_(k=1) ^n (1/(2 +(k/n))) ⇒ S_n is a Rieman sum and lim_(n→∞) S_n = ∫_0 ^1 (dx/(2+x)) =[ln∣2+x∣]_0 ^1 = ln3 −ln2 .

letputSn=∑k=1n12n+kSn=1n∑k=1n12+kn⇒SnisaRiemansumandlimn→∞Sn=∫01dx2+x=[ln∣2+x∣]01=ln3−ln2.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com