{:(" " Lt),(n rarroo):}(1)/(n^(2)) sum(r...

`{:(" " Lt),(n rarroo):}(1)/(n^(2)) sum_(r=1)^(n) r.e^(r//n)=`

A

e

B

1

C

2e

D

2

Text Solution

Verified by Experts

The correct Answer is:

B

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AAKASH SERIES-DEFINITE INTEGRALS-PRACTICE EXERCISE

{:(" " Lt),(n rarroo):} sum(r=1)^(n)(r)/(n^(2)+r^(2))=
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{:(" " Lt),(n rarroo):} 1/n sum(r=1)^(n)sqrt(r/n)=
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{:(" " Lt),(n rarroo):}(1)/(n^(2)) sum(r=1)^(n) r.e^(r//n)=
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Lt(ntooo){(1)/(n+1)+(1)/(n+2)+......+(1)/(2n)}=
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Lt(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=
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{:(" " Lt),(n rarroo):}1/n ((1)/(n+1) +(2)/(n+2)......+3/(4n))=
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{:(" " Lt),(n rarroo):} [(1)/(3n+1)+(1)/(3n+2)+.......+(1)/(4n)]=
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Lt(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=
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{:(" " Lt),(n rarroo):} ((1+8+27+.......+n^(3))/(n^(4)))=
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Lt(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=
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Lt(n rarr oo)[(1^(99)+2^(99)+3^(99)+...+n^(99))/(n^(100))]
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{:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+...
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Lt(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+n^(2))]
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{:(" " Lt),(n rarroo):} pi/n (sin. pi/n + sin. (2pi)/(n)+sin. (3pi)/(...
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{:(" " Lt),(n rarroo):} (pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)...
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Evaluate the following define integrals as limit of sums : lim(n rar...
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Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...
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Lt(ntooo){(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2)+2^(2)))+.......+(1)/(sqr...
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Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...
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Evaluate the following define integrals as limit of sums : lim(n rar...
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