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Let S(n)=underset(k=1)overset(n)sum (n)/...

Let `S_(n)=underset(k=1)overset(n)sum (n)/(n^(2)+nk+k^(2)) and T_(n)=underset(k=0)overset(n-1)sum(n)/(n^(2)+nk+k^(2))` for `n=1, 1,2,3...,` they

A

`S_(n) lt (pi)/(3 sqrt3)`

B

`S_(n) gt (pi)/(3 sqrt3)`

C

`T_(n) lt (pi)/(3 sqrt3)`

D

`T_(n)gt (pi)/(3 sqrt3)`

Text Solution

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The correct Answer is:
A, D
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ML KHANNA-DEFINITE INTEGRAL-Problem Set (6) Multiple choice Questions
  1. lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....

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

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

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  4. v20.1

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

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

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

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

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

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

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

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  12. 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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  13. 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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  14. Lt(n rarr oo) (2^(k) + 4^(k) + 6^(k) + …+ (2n)^(k))/(n^(k+1)) , k ne -...

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

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

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

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  18. Lt(n rarr oo) [(1)/(n^(2)) sin ((1+ n^(2))/(n^(2))) + (2)/(n^(2)) sin ...

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  19. Given that lim(nto oo) sum(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1...

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  20. Let S(n)=underset(k=1)overset(n)sum (n)/(n^(2)+nk+k^(2)) and T(n)=unde...

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