Home
Class 11
MATHS
underset(n to oo)lim (n(1^(3)+2^(3)+...+...

`underset(n to oo)lim (n(1^(3)+2^(3)+...+n^(3))^(2))/((1^(2)+2^(2)+...+n^(2))^(3))=`

Text Solution

Verified by Experts

The correct Answer is:
`(27)/(16)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE 1.1 (VERY SHORT ANSWER QUESTIONS)|23 Videos

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE 1.1 (SHORT ANSWER QUESTIONS)|18 Videos

  • LIMITS

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|33 Videos

  • INVERSET TRIGONOMETRIC FUNCTIONS

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL-II PRACTICE SHEET (ADVANCED) INTEGER TYPE QUESTIOS)|5 Videos

  • LOCUS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

Similar Questions

Explore conceptually related problems

underset(n to oo)lim (1^(3)+2^(3)+3^(3)+...+n^(3))/(n^(4))=

underset(n to oo)lim (1^(2)+2^(2)+3^(2)+...+n^(2))/(n^(3))=

underset(n to oo)lim (2^(n)-n)/(2^(n))=

underset(n to oo)lim (1+2+3+...+n)/(n^(2))=

underset(n to oo)lim (2^(n)-1)/(3^(n)+1)=

underset(n to oo)lim (5^(n)+1)/(3^(n)-1)=

underset(n to oo)lim 1/n^(4) [1^(2)+(1^(2)+2^(2))+....+(1^(2)+2^(2)+...+n^(2)]=

underset(n to oo)lim (1+3+3^(2)+...3^(n))/(1+2+2^(2)+...+2^(n))=

underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=

underset(n to oo)lim (3^(x+1)+4)/(3^(x+2)+4)=

AAKASH SERIES-LIMITS-SOLVED EXAMPLES
  1. Evulate Lt(x to 0)(27^(x)-9^(x)-3^(x)+1)/(x^(2))

    Text Solution

    |

  2. Evaluate Lt(xto0)((e^(x^(2))-cosx)/x^(2)).

    Text Solution

    |

  3. underset(n to oo)lim (n(1^(3)+2^(3)+...+n^(3))^(2))/((1^(2)+2^(2)+...+...

    Text Solution

    |

  4. underset(n to oo)lim {(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+....+(1)/((3n-2)(...

    Text Solution

    |

  5. Show that Lt(ntooo)(3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=-20/7

    Text Solution

    |

  6. Lt(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

    Text Solution

    |

  7. Evaulate Lt(x to 0)(1+ax)^(b//x) where a,b are constants.

    Text Solution

    |

  8. Evaluate Lt(xtooo)(1+1/(ax+b))^(cx+d) where a, b, c, d are positive co...

    Text Solution

    |

  9. Find Lt(x to 0)((sinx)/(x))^((sinx)/(x-sinx))

    Text Solution

    |

  10. Find Lt(xtooo)((x+a)/(x+b))^(x), a, b are constants.

    Text Solution

    |

  11. Evaluate Lt(xtooo)((x^(2)+ax+b)/(x^(2)+cx+d))^(x) where a, b, c, d are...

    Text Solution

    |

  12. Find Lt(x to oo)((3x^(2)+1)/(4x^(2)-1))^((x^(3))/(1+x)) Caution : Th...

    Text Solution

    |

  13. Evaluate Lt(xto0)((a^(x)+b^(x)+c^(x))/3)^(1/x) where a,b,cinR^(+).

    Text Solution

    |

  14. If Lt(x to 0)(1+ax+bx^(2))^(2//x)=e^(3), find an and b.

    Text Solution

    |

  15. Find Lt(xto0)((sinx-x+x^(3)/6)/x^(5))

    Text Solution

    |

  16. Find a, b and c if Lt(xto0)((ae^(x)-bcosx+ce^(-x))/x^(2))=2

    Text Solution

    |

  17. Evaluate Lt(x to 0)[((1+x)^((1)/(x))-e+(ex)/(2))/(sin^(2)x)]

    Text Solution

    |

  18. Find Lt(x to oo)([ax+b])/(x) (a gt 0) where [.] denotes the GIF.

    Text Solution

    |

  19. Show that Lt(ntooo)([x]+[2x]+...+[nx])/n^(2)=x/2.

    Text Solution

    |

  20. Show that Lt(x to oo)(x-logx)/(x+logx)=1

    Text Solution

    |