Home
Class 12
MATHS
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)/(3sqrt(3))`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

If S_(n) = underset (r=0) overset( n) sum (1) /(""^(n) C_(r)) and T_(n) = underset(r=0) overset(n) sum (r )/(""^(n) C_(r)) then (t_(n))/(s_(n)) = ?

The value of cot (underset(n=1)overset(23)sum cot^(-1) (1 + underset(k=1)overset(n)sum 2k)) is

Let S_(k)=underset(ntooo)limunderset(i=0)overset(n)sum(1)/((k+1)^(i))." Then "underset(k=1)overset(n)sumkS_(k) equals

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

underset(r=1)overset(n-1)(sum)cos^(2)""(rpi)/(n) is equal to

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-n^(2)) is equal to

If f(x) = (a^(x))/(a^(x) + sqrt(a)), a gt 0 prove that (i) f(x) + f(1-x) = 1 (ii) underset(k=1)overset(2n-1)sum 2f ((k)/(2n)) = 2n-1 (iii) underset(k=1)overset(2n)sum 2f((k)/(2n+1)) = 2n

If underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007! , then value of n is

Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

    Text Solution

    |

  2. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

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

    Text Solution

    |

  4. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle....

    Text Solution

    |

  9. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  10. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  11. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  12. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  13. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

  14. The area of the region between the curves y=sqrt((1+sinx)/(cos x)) and...

    Text Solution

    |

  15. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  16. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

    Text Solution

    |

  17. For which of the following values of m is the area of the regions boun...

    Text Solution

    |

  18. If [4a2 4a 1 4b2 4b 1 4c2 4c 1] [f-1 f1 f2] = [3a2 + 3a 3b2 + 3b 3c2 +...

    Text Solution

    |

  19. Find the area bounded by the curve x^2=y ,x^2=-ya n dy^2=4x-3

    Text Solution

    |

  20. A curve C passes through (2,0) and the slope at (x , y) as ((x+1)^2...

    Text Solution

    |