Home
Class 11
MATHS
lim(n->oo)(1^2+2^2+3^2+..........+n^2)/n...

`lim_(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3`

Text Solution

Verified by Experts

`lim_(x->infty) (1^2+2^2+3^2+..........+n^2)/n^3`
`= lim_(x->infty) {{n(n+1)(2n+1)}/6}/n^3`
`=lim_(x->infty) {n(n+1)(2n+1)}/{6n^3}`
`=lim_(x->infty) {n^3(1+1/n)(2+1/n)}/{6n^3}`
`=lim_(x->infty) {(1+1/n)(2+1/n)} /6`
`=1/3`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

lim_(n rarr oo)(1^(2)+2^(2)+3^(2)+.........+n^(2))/(n^(3)) is equal to -

Evaluate: lim_(n rarr oo)(1^(2)+2^(2)+......+n^(2))/(n^(3))

Evaluate: lim_(n rarr oo)(1^(2)+2^(2)+......+n^(2))/(n^(3))

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

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

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

lim_(n to oo) (1^(2)+2^(2)+3^(2)+…+n^(2))/(n^(3)) is equal to

(lim_(n rarr oo)(1^(2)+2^(2)+3^(2)++n^(2))/(n^(3)) is equal to a.1b*c*1/3d.0

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

Evaluate: lim_(n rarr oo) ((1^(2)+2^(2)+3^(2)+...+n^(2)))/((1+3+5+7+...+"n terms")) .

RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: lim(x->oo)(sqrt(x^2+a^2)-sqrt(x^2+b^2))/...

    Text Solution

    |

  2. lim(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

    Text Solution

    |

  3. lim(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

    Text Solution

    |

  4. Evaluate the following limit: lim(x->0)(x^2)/(sin x^2)

    Text Solution

    |

  5. Evaluate the following limit: lim(x->0)(sinxcosx)/(3x)

    Text Solution

    |

  6. Evaluate the following limit: lim(x->0)(3sin x-4sin^3x)/x

    Text Solution

    |

  7. lim(x->0)(tanm x)/(tann x)

    Text Solution

    |

  8. Evaluate the following limit: (lim)(x->0)(sinx^0)/(x^0)

    Text Solution

    |

  9. Evaluate the following limit: (lim)(x->0)(cos a x-cos b x)/(cosc x-cos...

    Text Solution

    |

  10. Evaluate the following limit: (lim)(x->0)(1-cosm x)/(x^2)

    Text Solution

    |

  11. Evaluate the following limit: (lim)(x->0)(cos3x-cos7x)/(x^2)

    Text Solution

    |

  12. Evaluate the following limit: (lim)(x->0)(xcosx+2\ sin x)/(x^2+tanx)

    Text Solution

    |

  13. Evaluate the following limit: (lim)(x->0)(5xcosx+3sinx)/(3x^2+tanx)

    Text Solution

    |

  14. Evaluate the following limit: (lim)(x->0)(sin5x-sin3x)/(sinx)

    Text Solution

    |

  15. Evaluate lim(x-> 0) (tan3x-2x)/(3x- sin^2 x)

    Text Solution

    |

  16. lim(x->0)(1-cos2x+tan^2x)/(xsinx)

    Text Solution

    |

  17. Evaluate the following limit: (lim)(x->0)(x^2-t a n2x)/(t a n x)

    Text Solution

    |

  18. Evaluate the following limit: (lim)(x->0)(xtanx)/(1-cos x)

    Text Solution

    |

  19. Evaluate the following limit: (lim)(x->0)(sin2x(cos3x-3cos x))/(x^3)

    Text Solution

    |

  20. Evaluate the following limit: (lim)(x->0)(x^3cotx)/(1-cos x)

    Text Solution

    |