Home
Class 11
MATHS
Prove that 1+(1)/(4)+(1)/(9)+..............

Prove that `1+(1)/(4)+(1)/(9)+...........+(1)/(n^(2))lt2-(1)/n,(ngt1)`

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    V PUBLICATION|Exercise QUESTIONBANK|79 Videos

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|89 Videos

Similar Questions

Explore conceptually related problems

Prove that 1(1) !+2(2) !+3(3) !+............ .+n(n) ! = (n+1) !-1

Prove that ((n+1)/(2))^(n) gt (n!)

Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+.......+1/((3n-2)(3n+1))=n/(3n+1) for all n in N

For all nge1 , prove that 1/1.2+1/2.3+1/3.4+..........+1/(n(n+1))=n/(n+1)

For all n gt 1 , prove that 1^(2)+2^(2)+3^(2)+4^(2)+...........+n^(2) = (n(n+1)(2 n+1))/(6)

Using mathematical induction prove that 1/(3.5)+1/(5.7)+1/(7.9)+.......+1/((2n+1)(2n+3))=n/(3(2n+3) for all n in N

Using mathematical induction prove that 1/(1.2.3)+1/(2.3.4)+......+1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2)) for all n in N .

Using mathematical induction prove that (1+3/1)(1+5/4)(1+7/9)......(1+(2n+1)/n^2)=(n+1)^2 for all n in N

For all nge1 , prove that 1+1/((1+2))+1/((1+2+3))+.......+1/((1+2+3+....+n))=(2n)/((n+1))

For all nge1 , prove that 1/1.3+1/3.5+1/5.7+......+1/((2n-1)(2n+1))=n/(2n+1)

V PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+......

    Text Solution

    |

  2. Using mathematical induction prove that 1/(3.5)+1/(5.7)+1/(7.9)+.......

    Text Solution

    |

  3. For all nge1,prove that 1+2+3+……+nlt1/8(2n+1)^2

    Text Solution

    |

  4. Using principle of mathematical induction prove that n(n+1)(n+5) is a ...

    Text Solution

    |

  5. Using mathematical induction prove that 10^(2n-1)+1 is divisible by 1...

    Text Solution

    |

  6. Using mathematical induction prove that x^(2n)-y^(2n) is divisible by ...

    Text Solution

    |

  7. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Verify...

    Text Solution

    |

  8. Using mathematical induction prove that 41^n-14^n is a multiple of 2...

    Text Solution

    |

  9. Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in...

    Text Solution

    |

  10. Using mathematical induction prove that P(n) = 1+3+5+........... +2n-1...

    Text Solution

    |

  11. Observe the following pattern of dots i) Find the number of dots i...

    Text Solution

    |

  12. If P(n) is the statement n(n+1) is even then what about P(6)?

    Text Solution

    |

  13. If P(n) is the statement n(n+1)(n+2) is divisiblé by 12, prove that P...

    Text Solution

    |

  14. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assum...

    Text Solution

    |

  15. Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

    Text Solution

    |

  16. Prove by mathematical induction. (costheta +i sintheta)^n=(cosntheta...

    Text Solution

    |

  17. Prove that 1(1) !+2(2) !+3(3) !+............ .+n(n) ! = (n+1) !-1

    Text Solution

    |

  18. Prove that 1+(1)/(4)+(1)/(9)+...........+(1)/(n^(2))lt2-(1)/n,(ngt1)

    Text Solution

    |

  19. Using principle of mathematical induction, prove that the product of t...

    Text Solution

    |

  20. Using mathematical induction prove that 1cdot3+3cdot5+5cdot7+.....+(...

    Text Solution

    |