Home
Class 11
MATHS
Using principle of mathematical inductio...

Using principle of mathematical induction, prove that
`(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+. . . . +(1)/(n(n+1))=(n)/(n+1)`

Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise EXERCISE|85 Videos

  • LINEAR INEQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE|289 Videos

  • MATHEMATICAL MODELLING

    MODERN PUBLICATION|Exercise EXAMPLE|3 Videos

Similar Questions

Explore conceptually related problems

By Mathematical Induction, prove that : n! 1 .

Using principle of mathematical induction, prove that: 1+3+5+………..+(2n-1)= n^2 .

Use principle of mathematical induction to prove that: 1+2+3+……….+n=(n(n+1))/2

Prove the following by using the principle of mathematical induction for all n in N :- 1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...+1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2)) .

Prove the following by using the principle of mathematical induction for all n in N :- (1+1/1)(1+1/2)(1+1/3)...(1+1/n)=(n+1) .

By Principle of Mathematical Induction, prove that : 2^n >n for all n in N.

Prove the following by using the principle of mathematical induction for all n in N :- 1.2 + 2.3 + 3.4 +... +n.(n+1)=[(n(n+1)(n+2))/3]

Prove the following by using the principle of mathematical induction for all n in N :- (1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/n^2)=(n+1)^2.

MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Using principle of mathematical induction, prove that (1)/(1.2)+(1)/...

    Text Solution

    |

  2. Let P (n) be the statement : “P(n) : 10n + 3 is prime’’. Is P(3) true...

    Text Solution

    |

  3. Let P(n) be the statement ''2^n > 1’’. Is P(1) true ?

    Text Solution

    |

  4. If P(n) is the statement “n(n + 1) is even’’, then what is P(4) ?

    Text Solution

    |

  5. Let P(n) be the statement ''n^3 +n is divisible by 3”. Is the statem...

    Text Solution

    |

  6. Let P(n) be the statement ''n^3 +n is divisible by 3”. Is the statem...

    Text Solution

    |

  7. If P(n) is the statement ‘‘n^2 > 100” prove that P(r + 1) is true when...

    Text Solution

    |

  8. If P(n) is the statement ‘‘2^n ge n’’, prove that P(r +1) is true when...

    Text Solution

    |

  9. Let P(n) be the statement ‘‘4^n > n’’. If P(r) is true, prove that P(r...

    Text Solution

    |

  10. If P(n) is the statement ''2^(3n)-1 is an integral multiple of 7", pro...

    Text Solution

    |

  11. If P(n) is the statement “sum of first n natural numbers is divisible ...

    Text Solution

    |

  12. Give an example of a statement P(n), which is true for all n ge 4, but...

    Text Solution

    |

  13. Give an example of the following statement : P(n) such that it is true...

    Text Solution

    |

  14. Give an example of the following statement : P(n) such that P(3) is tr...

    Text Solution

    |

  15. If P(n) is the statement : ''^nCr len ! for 1 le r len ", then : find ...

    Text Solution

    |

  16. If P(n) is the statement : ''^nCr len ! for 1 le r len ", then : show ...

    Text Solution

    |

  17. Prove that the Principle of Mathematical Induction does not apply to t...

    Text Solution

    |

  18. Prove that the Principle of Mathematical Induction does not apply to t...

    Text Solution

    |

  19. By the Principle of Mathematical Induction, prove the following for al...

    Text Solution

    |

  20. By the Principle of Mathematical Induction, prove the following for al...

    Text Solution

    |

  21. By the Principle of Mathematical Induction, prove the following for al...

    Text Solution

    |