Home
Class 11
MATHS
underset(n to oo)lim {(1)/(1.3)+(1)/(3.5...

`underset(n to oo)lim {(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/((2n-1)(2n+1))}=`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(6)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE-I|48 Videos

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE-II|100 Videos

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE 1.5 ( SHORT ANSWER QUESTIONS)|4 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)/(1.4)+(1)/(4.7)+(1)/(7.10)+....+(1)/((3n-2)(3n+1))}=

underset(n to oo)lim {(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))}=

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

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

(1)/(1.3) + (1)/(3.5) + (1)/(5.7) + …. (n-3) terms

Lt_(x to oo)((1)/(3.5)+(1)/(5.7)+.....+(1)/((2n+1)(2n+3)))=

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

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

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

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

AAKASH SERIES-LIMITS-ADDITIONL EXERCISE
  1. underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=

    Text Solution

    |

  2. Evaluate the following limits: lim(x to oo) ((1)/(3)+(1)/(3^(2))+......

    Text Solution

    |

  3. underset(n to oo)lim {(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/((2n-1)(...

    Text Solution

    |

  4. Evaluate the following limits: lim(x to oo)(q^(n)+p^(n))^(1//n), 0 l...

    Text Solution

    |

  5. Evaluate the following limits: lim(x to 0) (e^(2x)-e^(3x))/(x)

    Text Solution

    |

  6. Evaluate the following limits: lim(x to 0) (x(3^(x)-1))/(1-cosx)

    Text Solution

    |

  7. Evaluate the following limits: lim(x to 0) (e^(sin^(2)x)-1)/(x^(2))

    Text Solution

    |

  8. Evaluate the following limits: lim(x to0) (1+x)^(3//x)

    Text Solution

    |

  9. Evaluate the following limits: lim(x to0) (1+3x)^(4//x)

    Text Solution

    |

  10. Evaluate the following limits: lim(x to oo) (1+(2)/(x))^(3x)

    Text Solution

    |

  11. Evaluate the following limits: lim(x to 0)(cos x+sinx)^(1//x)

    Text Solution

    |

  12. Evaluate the following limits: lim(x to0)((1+tanx)/(1+sinx))^("cosec...

    Text Solution

    |

  13. underset(x to oo)"Lt" ((x+6)/(x+1))^(x+4)=

    Text Solution

    |

  14. Evaluate the following limits : Lt(xto7/2)(2x^(2)-9x+8)^(cot(2x-7))

    Text Solution

    |

  15. Evaluate the following limits: lim(x to oo )((x^(2)+2x+3)/(2x^(2)+x+...

    Text Solution

    |

  16. Evaluate the following limits: lim(x to oo) ((1^(x)+2^(x)+....+n^(x)...

    Text Solution

    |

  17. Evaluate the following limits: lim(x to0) (tanx-x)/(x^(3))

    Text Solution

    |

  18. Evaluate the following limits: lim(x to 0)(sin^(-1)x-tan^(-1)x)/(x^(...

    Text Solution

    |

  19. Evaluate the following limits: lim(x to 0)((1+x)^(1//x)-e)/(x)

    Text Solution

    |

  20. Evaluate the following limits: lim(x to 0)((1+x)^(1//x)-e+(ex)/(2))/...

    Text Solution

    |