Home
Class 12
MATHS
Iim(n to oo) (1^(99) + 2^(99) + …..+ n^(...

`Iim_(n to oo) (1^(99) + 2^(99) + …..+ n^(99))/(n^(100))` equals :

A

`99/100`

B

`1/100`

C

`1/99`

D

`1/101`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (LEVEL - II)|42 Videos

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise LATEST QUESTIONS FROM AIEEE/JEE EXAMINATION|13 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise Questions from karnataka CET & COMED|15 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

Similar Questions

Explore conceptually related problems

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

lim_(n to oo) (sqrt(1) + sqrt(2) + …… + sqrt(n))/(n^(3//2)) equals :

Lt_(n to oo)(1 + 2/n)^(2n) =

The value of lim_(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - lim_(n rarr oo) (1 + 2^(3) + 3^(3) +…...+n^(3))/(n^(5)) is :

lim_(n rarr oo) 1/n^(100) (1^(99)+2^(99)+3^(99)+………+n^(99)) =

Let a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))= , b = lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))= then

lim_(n rarr oo) [(1)/(1-n^(4))+(8)/(1-n^(4))+…...+(n^(3))/(1-n^(4))] equals :

lim_(n rarr oo) (1^(2)+2^(2)+....+n^(2))/(2n^(3)+3n^(2)+4n+1 ) =

lim_(n rarr oo) ((1)/(1-n^(2)) + (2)/(1-n^(2)) +…...+(n)/(1-n^(2))) is :

MODERN PUBLICATION-DEFINITE INTEGRALS-RECENT COMPETITIVE QUESTIONS
  1. Iim(n to oo) (1^(99) + 2^(99) + …..+ n^(99))/(n^(100)) equals :

    Text Solution

    |

  2. The value of the integral int0^(pi//2) (sin^(100) x - cos^(100) x) dx ...

    Text Solution

    |

  3. If [x] denote the greatest integer function , then , int(0)^(pi//6) (1...

    Text Solution

    |

  4. If [x] denotes the greatest integer function, then : ""(2)^(4)([x] -...

    Text Solution

    |

  5. int1^(e^(17//2)) (cos(pi log x))/(x) dx =

    Text Solution

    |

  6. int0^1 x(1 - x)^(3//2) dx =

    Text Solution

    |

  7. int0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

    Text Solution

    |

  8. int0^1 (x^4 + 2x^2 + 1)d(x^2 + 1) =

    Text Solution

    |

  9. If I(1)= int(0)^(pi//2) x sin x dx and I(2)=int(0)^(pi//2) x cos x dx,...

    Text Solution

    |

  10. The value of int(-1)^(2) (|x|)/(x) dx is :

    Text Solution

    |

  11. int0^pi (cos^4 x)/(cos^4 x + sin^4 x) dx =

    Text Solution

    |

  12. If f(x) = f(pi + e - x) and inte^(pi) f(x) dx = 2/(e + pi), then inte^...

    Text Solution

    |

  13. The value of the integral int(-pi//4)^(pi//4)log(sec theta-tan theta...

    Text Solution

    |

  14. The interval I such that int0^1 (dx)/(sqrt(1 + x^4)) in I is given by ...

    Text Solution

    |

  15. int0^(pi//2) log(tan x)dx =

    Text Solution

    |

  16. The value of int(-2)^(2)(ax^(3)+bx+c) dx depends on the

    Text Solution

    |

  17. int(0)^(pi//4)log ((sin x +cos x )/(cosx))dx is equal to

    Text Solution

    |

  18. int(-pi//4)^(pi//4)(dx)/(1+cos 2x) is equal to

    Text Solution

    |

  19. int(-1)^(1) (x^(27) cos x + e^x) dx =

    Text Solution

    |

  20. The value of the integral int0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n...

    Text Solution

    |

  21. If int0^(pi) x f (sin x) dx = A int0^(pi//2) f (sin x) dx, then A is :

    Text Solution

    |