2019 AP Calculus BC.1: Which is equal to lim _n →∞1/n(1/2+1/n+1/2+2/n+1/2+3/n+⋯+1/2+n/n)?

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lim n tends to infinity (1/1+n + 1/2+n + 1/3+n+......+1/2n) is equal to #iitjeemains2023lim n tends to infinity (1/1+n + 1/2+n + 1/3+n+......+1/2n) is equal to #iitjeemains2023
Evaluate: Lim(n→∞)[{(1+1/n)(1+2/n)(1+3/n)........(1+n/n)}^1/n]Evaluate: Lim(n→∞)[{(1+1/n)(1+2/n)(1+3/n)........(1+n/n)}^1/n]
EVALUATE: lim(n→∞) [(1+1/n)^1/1.(1+2/n)^1/2.(1+3/n)^1/3........(1+n/n)^1/n]EVALUATE: lim(n→∞) [(1+1/n)^1/1.(1+2/n)^1/2.(1+3/n)^1/3........(1+n/n)^1/n]
EVALUATE: Lim(n→∞)[1/n+1/(n+1)+1/(n+2)+......+1/3n]EVALUATE: Lim(n→∞)[1/n+1/(n+1)+1/(n+2)+......+1/3n]
This is a very famous limitThis is a very famous limit
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EVALUATE: lim(n→∞}[{(1+1/n²)(1+2²/n²)(1+3²/n²).......(1+n²/n²)}^1/n]EVALUATE: lim(n→∞}[{(1+1/n²)(1+2²/n²)(1+3²/n²).......(1+n²/n²)}^1/n]