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Question Number 112492 by mathdave last updated on 08/Sep/20

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

evaluatelimn→∞∑nk=11n+k2

Answered by Ar Brandon last updated on 08/Sep/20

1≤k≤n⇒1≤k^2 ≤n^2 ⇒n+1≤n+k^2 ≤n+n^2 ⇒(1/(n+n^2 ))≤(1/(n+k^2 ))≤(1/(n+1))⇒lim_(n→∞) Σ_(k=1) ^n (1/(n+n^2 ))≤lim_(n→∞) A_n ≤lim_(n→∞) Σ_(k=1) ^n (1/(n+1)) ⇒lim_(n→∞) (n/(n+n^2 ))≤lim_(n→∞) A_n ≤lim_(n→∞) (n/(n+1))⇒0≤lim_(n→∞) ≤1 ...

1⩽k⩽n⇒1⩽k2⩽n2⇒n+1⩽n+k2⩽n+n2Double subscripts: use braces to clarifyDouble subscripts: use braces to clarify...

Commented by mathdave last updated on 08/Sep/20

nice attempt

niceattempt

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