Home
Class 12
MATHS
{:(" "Lt),(n rarr oo):} (2^(k)+4^(k)+6^(...

`{:(" "Lt),(n rarr oo):} (2^(k)+4^(k)+6^(k)+....+(2n)^(k))/(n^(k+1))=`

A

`(2^(k))/(k+1)`

B

`(4^(k))/(k+1)`

C

`(1)/(k+1)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|151 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Examples|8 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - I|67 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

{:(" "Lt),(n rarr oo):} ((1+2^(4)+3^(4)+......+n^(4))/(n^(5)))-{:(" "Lt),(n rarr oo):} ((1+2^(3)+3^(3)+....+n^(3))/(n^(5)))=

Evaluate lim_(n rarr oo)(2^(k) + 4^(k) + 6^(k)+…+(2n)^(k))/(n^(k+1)) by using the method of finding definite integral as the limit of a sum.

lim_(n toinfty)[(1^(k) +2^(k)+3^(k) +. . .. +n^(k))/(n^(k +1))]=

{:(" "Lt),(n rarr oo):} [(1)/(1-n^(2))+(2)/(1-n^(2))+...+(n)/(1-n^(2))]=

{:(" "Lt),(n rarr oo):}(1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}=

{:(" "Lt),(n rarr oo):} 1/n sum_(r=1)^(n)sec^(2).(rpi)/(4n)=

{:(" "Lt),(n rarr oo):}{ (1)/(2n+1)+(1)/(2n+2)+......+(1)/(3n)}=

AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. {:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1))...

    Text Solution

    |

  2. {:(" "Lt),(n rarr oo):} ((1+2^(4)+3^(4)+......+n^(4))/(n^(5)))-{:(" "L...

    Text Solution

    |

  3. {:(" "Lt),(n rarr oo):} (2^(k)+4^(k)+6^(k)+....+(2n)^(k))/(n^(k+1))=

    Text Solution

    |

  4. Lt(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2...

    Text Solution

    |

  5. Lt(ntooo){(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+.......+1/(n)}

    Text Solution

    |

  6. {:(" "Lt),(n rarr oo):} [ (1)/(n^(2)) sec^(2). (1)/(n^(2)) + (2)/(n^(2...

    Text Solution

    |

  7. {:(" "Lt),(n rarr oo):} ((sqrt(1)+2sqrt(2)+3sqrt(3)+......+nsqrt(n))/(...

    Text Solution

    |

  8. {:(" "Lt),(n rarr oo):} [(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)...

    Text Solution

    |

  9. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-2^(2)))...

    Text Solution

    |

  10. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+(1)...

    Text Solution

    |

  11. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+n))+(1)/(sq...

    Text Solution

    |

  12. Lt(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2))/((n+3)^(3//2))+(n^(1//2))/(...

    Text Solution

    |

  13. If S(n)={(1)/(1+sqrt(n))+(1)/(2+sqrt(2n))+(1)/(3+sqrt(3n))+....+(1)/(n...

    Text Solution

    |

  14. {:(" "Lt),(n rarr oo):} 3/n [1 + sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt(...

    Text Solution

    |

  15. {:(" "Lt),(n rarr oo):} ((n!)/(n^(n)))^(1/n)=

    Text Solution

    |

  16. Evaluate the limit . underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^...

    Text Solution

    |

  17. If f(n)= 1/n {(n+1)(n+2)....2n}^(1//n) then {:(" "Lt),(n rarr oo):} f(...

    Text Solution

    |

  18. {:(" "Lt),(n rarr oo):}(((2n)!)/(n!n^(n)))^(1/n)=

    Text Solution

    |

  19. The solution for x of the equation int(sqrt(2))^(x) (dt)/(|t|sqrt(t^(2...

    Text Solution

    |

  20. int(0)^(1)(dx)/(x+sqrt(x))=

    Text Solution

    |