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Lt(ntooo)sum(r=1)^(n)(1)/(sqrt(4n^(2)-r^...

`Lt_(ntooo)sum_(r=1)^(n)(1)/(sqrt(4n^(2)-r^(2)))=`

A

`pi`

B

`pi/2`

C

`pi/3`

D

`pi/6`

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-DEFINITE INTEGRALS-PRACTICE EXERCISE
  1. Lt(ntooo)sum(r=0)^(n-1)(1)/(n+r)=

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  2. Lt(ntooo)sum(r=0)^(n-1)(n)/(n^(2)+r^(2))=

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  3. Lt(ntooo)sum(r=1)^(n)(1)/(sqrt(4n^(2)-r^(2)))=

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

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

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

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  7. Lt(ntooo){(1)/(n+1)+(1)/(n+2)+......+(1)/(2n)}=

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  8. Lt(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=

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  9. {:(" " Lt),(n rarroo):}1/n ((1)/(n+1) +(2)/(n+2)......+3/(4n))=

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  10. {:(" " Lt),(n rarroo):} [(1)/(3n+1)+(1)/(3n+2)+.......+(1)/(4n)]=

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  11. Lt(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=

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  12. {:(" " Lt),(n rarroo):} ((1+8+27+.......+n^(3))/(n^(4)))=

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  13. Lt(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=

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  14. Lt(n rarr oo)[(1^(99)+2^(99)+3^(99)+...+n^(99))/(n^(100))]

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  15. {:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+...

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  16. Lt(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+n^(2))]

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  17. {:(" " Lt),(n rarroo):} pi/n (sin. pi/n + sin. (2pi)/(n)+sin. (3pi)/(...

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  18. {:(" " Lt),(n rarroo):} (pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)...

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  19. Evaluate the following define integrals as limit of sums : lim(n rar...

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  20. Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...

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