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The value of lim(n to oo)[(n)/(n^(2))+(n...

The value of `lim_(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+(n-1)^(2))]` is :

A

`pi`

B

`(pi)/(2)`

C

`(pi)/(3)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
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ML KHANNA-DEFINITE INTEGRAL-Problem Set (6) Multiple choice Questions
  1. lim(n rarr oo) [(1)/(sqrt""(n^(2)-1)) + (1)/(sqrt""(n^(2) - 2^(2)))+ …...

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  2. The value of lim(n to oo)sum(r=1)^(n)(1)/(n) sqrt(((n+r)/(n-r))) is :

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  3. The value of lim(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(...

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  4. lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....

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  5. underset(n to oo)"lim"underset(r=1)overset(n)sum((r^(3))/(r^(4) + n^(4...

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  6. underset(nrarroo)lim[(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+....

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  7. v20.1

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  8. Evaluate: (lim)(nvecoo)([(n+1)(n+2)(n+n)^(1/n))/n

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  9. The value of lim(n rarr oo) [((2n)!)/(n!n^(n))]^(1//n) is equal to

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  10. Lim(n rarr oo)[(1)/(1-n^(2))+(2)/(1-n^(2))+.....+(n)/(1-n^(2))] is equ...

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  11. lim(n rarr oo) (1)/(n) ["tan"(pi)/(4n) + "tan"(2pi)/(4n) + …+ "tan"(n ...

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  12. The value of lim(nrarroo)(1)/(n)[sec^(2)""(pi)/(4n)+sec^(2)""(2pi)/(4n...

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  13. Evaluate: ("lim")(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/...

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  14. lim(n rarr oo) (1^(99) + 2^(99) + …+ n^(99))/(n^(100))=

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  15. Lt(nrarroo) (1+2^4+3^4+ … +n^4)/n^5-Lt(nrarroo) (1+2^3+3^3 + … +n^3)/n...

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  16. Lt(nrarroo) (1+2^4+3^4+ … +n^4)/n^5-Lt(nrarroo) (1+2^3+3^3 + … +n^3)/n...

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  17. Lt(n rarr oo) (2^(k) + 4^(k) + 6^(k) + …+ (2n)^(k))/(n^(k+1)) , k ne -...

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  18. underset(n to oo)lim(1)/(2)" " underset(r=+1)overset(2n)sum (r)/(s...

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  19. Lt(n rarr oo) Sigma(r=1)^(n-1) (pi)/(n) sin ((r pi)/(n))=

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  20. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

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