Home
Class 12
MATHS
For a epsilonR (the set of all real numb...

For `a epsilonR` (the set of all real numbers) `a!=-1, lim_(n to oo) ((1^(a)+2^(a)+………+n^(a)))/((n+1)^(a-1)[(na+1)+(n+2)+………..+(na+n)])=1/60`
Then `a=`

A

5

B

7

C

`(-15)/(2)`

D

`(-17)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

Find a for which lim_(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+(na+2)+...+(na+n)])=1/60

lim_(n to oo)(n!)/((n+1)!-n!)

lim_(n->oo) nsin(1/n)

lim_(n to oo)(1-2n^(2))/(5n^(2)-n+100)=

lim_(n to oo) sum_(r=1)^(n) (1)/(n)e^(r//n) is

lim_(n rarr oo)((n+1)^(4)-(n-1)^(4))/((n+1)^(4)+(n-1)^(4))

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

lim_(n rarr oo)2^(1/n)

lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=

lim_(n->oo)2^(n-1)sin(a/2^n)

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  2. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  5. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  6. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  7. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

    Text Solution

    |

  8. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  9. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  10. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

    Text Solution

    |

  11. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  12. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  13. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  14. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  15. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  16. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  17. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  18. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  19. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

    Text Solution

    |

  20. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |