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Let Sn=sum(k=0)^n n/(n^2+k n+k^2) and ...

Let `S_n=sum_(k=0)^n n/(n^2+k n+k^2) and T_n=sum_(k=0)^(n-1)n/(n^2+k n+k^2)`,for `n=1,2,3,.......,` then

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

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  2. Consider the statements : P : There exists some x IR such that f(x)...

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  3. Which of the following is true?

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  4. For any real number x ,l e t[x] denote the largest integer less than o...

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  5. Let f be a non-negative function defined on the interval .[0,1].If int...

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  6. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

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  7. Let Sn=sum(k=0)^n n/(n^2+k n+k^2) and Tn=sum(k=0)^(n-1)n/(n^2+k n+k...

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  8. The Integral int(pi/4)^((3pi)/4)(dx)/(1+cosx) is equal to: ...

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  9. Let In=int tan^n x dx, (n>1). If I4+I6=a tan^5 x + bx^5 + C, Where C...

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  10. lim(n rarr infty ) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is equal to

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  11. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

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  12. The integral int(0)^(pi) sqrt(1+4 sin )(x)/(2) -4 "sin" (x)/(2) dx is...

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  13. Statement I The value of the integral int(pi//6)^(pi//3) (dx)/(1+sqrt...

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  14. The intercepts on x-axis made by tangents to the curve, y=int0^x|t|...

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  15. Ifg(x)= int(0)^(x) cos ^(4)t dt, "then " g (x+pi) equals

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  16. The value of int(0)^(1) (8 log(1+x))/(1+x^(2)) dx is

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  17. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

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  18. Let p(x) be a function defined on R such that lim(xrarr infty) f (3x...

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  19. int(0)^(pi)[cos x] dx, [ ] denotes the greatest integer function , is ...

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  20. Let I=int(0)^(1)(sinx)/(sqrtx) dx and f= int(0)^(1)( cos x)/(sqrtx) dx...

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