Home
Class 11
MATHS
Let Sk=underset(nrarrinfty)limsum(i=0)^n...

Let `S_k=underset(nrarrinfty)limsum_(i=0)^n1/(k+1)^i.` Then `sum_(k=1)^nkS_k` equals

A

`(n(n+1))/2`

B

`(n(n-1))/2`

C

`(n(n+2))/2`

D

`(n(n+3))/2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

sum_(i = 1)^n sum_(j = 1)^i sum_(k = 1)^j 1 is equal to

sum_(k=1)^ook(1-1/n)^(k-1) =?

Let f(x) be a continous function defined on the closed interval [a,b] then underset(nrarrinfty)limsum underset(r=0)overset(n-1) (1/n)f(r/n)=int_0^1f(x)dx The value of underset(nrarrinfty)limunderset(r=1)oversetnsum (1+(r/n))(1/n) is

underset(nrarrinfty)lim((n+1)(n+2)....3n)/(n^(2n)))^(1/n) is equal to

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

If underset(xrarr0)"lim" (1-cos4x)/(1-cos6x)=(4)/(K) then K is equal to -

Let S_k be the sum of an infinite G.P. series whose first term is k and common ratio is k/(k+1) (k gt 0) . Then the value of sum_(k = 1)^infty (-1)^k/s_k is equal to

Evaluate : underset (nrarrinfty)lim underset(r=0)overset(n-1)sum 1/sqrt(4n^2-r^2)

The sum sum_(k=1)^(10)underset(i ne j ne k)underset(j=1)(sum^(10))sum_(i=1)^(10)1 is equal to

Evaluate sum_(k=1)^11(2+3^k)

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If (1+x)(1+x^2)(1+x^4)....(1+x^128)=sum(r=0)^nx^r then n is

    Text Solution

    |

  2. If angt1 for all ninN,then log(a2)a1+log(a3)a2+.....+log(an)a(n-1)+log...

    Text Solution

    |

  3. Let Sk=underset(nrarrinfty)limsum(i=0)^n1/(k+1)^i. Then sum(k=1)^nkSk...

    Text Solution

    |

  4. If a1,a2,a3...an are in HP and f(k)=sum(r=1)^nar-ak, then a1/(f(1)),a...

    Text Solution

    |

  5. sum(r=1)^nr^2-sum(m=1)^nsum(r=1)^mr is equal to

    Text Solution

    |

  6. The sum of the integer from 1 to 100 which is not divisible by 3 or 5 ...

    Text Solution

    |

  7. If ab^2c^3,a^2b^3c^4,a^3b^4c^5 are in AP (a,b,cgt0) thgen the minimum...

    Text Solution

    |

  8. If the sum of n terms of the series 1/1^3+(1+2)/(1^3+2^3)+(1+2+3)/(1^3...

    Text Solution

    |

  9. The coefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)....(x-n) ...

    Text Solution

    |

  10. The series of natural number is divided into groups as follows , (1), ...

    Text Solution

    |

  11. The sum of 10 terms of the series (x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)...

    Text Solution

    |

  12. If the sequence 1,2,2,4,4,4,4,,8,8,8,8,8,8,8,8,.... where n consecutiv...

    Text Solution

    |

  13. Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+.... is

    Text Solution

    |

  14. The cubes of the natural numbers are grouped as 1^3,(2^3,3^3),(4^3,5^3...

    Text Solution

    |

  15. Let f(n)=[1/2+n/100] where [x] denote the integral part of x. Then th...

    Text Solution

    |

  16. ABC is a right angled triangle in which angleB=90^@ and BC=a. If n poi...

    Text Solution

    |

  17. If a,b,c are three distinct positive real number such that a^2+b^2+c^2...

    Text Solution

    |

  18. The sum of the series 1^3 - 2^3 + 3^3 - ....+ 9^3=

    Text Solution

    |

  19. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

    Text Solution

    |

  20. Let two numbers have arithmetic mean 9 and geometric mean 4. Then thes...

    Text Solution

    |