Home
Class 11
MATHS
By the Principle of Mathematical Inducti...

By the Principle of Mathematical Induction, prove the following for all n `in` N :
`1+3+5+....... +(2n-1) =n^2` i.e. the sum of first » odd natural numbers is `n^2` .

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 the Principle of Mathematical Induction, prove the following for all n in N : 4+8+ 12+......+ 4n= 2n(n + 1) .

By the Principle of Mathematical Induction, prove the following for all n in N : n^2-n+41 is prime.

By the Principle of Mathematical Induction, prove the following for all n in N : 1+4+7+.....+ (3n-2)= (n(3n-1))/2 .

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

By the Principle of Mathematical Induction, prove the following for all n in N : 1^2+2^2+3^2+ .......... + n^2> n^3/3 .

By the Principle of Mathematical Induction, prove the following for all n in N : 5+15+45+.....+5 (3)^(n-1) = 5/2 (3^n-1) .

By the Principle of Mathematical Induction, prove the following for all n in N : 5^(2n)-1 is divisible by 24.

By the Principle of Mathematical Induction, prove the following for all n in N : 3^(2n)-1 is divisible by 8 .

By the Principle of Mathematical Induction, prove the following for all n in N : 15^(2n-1)+1 is multiple of 16.

By the Principle of Mathematical Induction, prove the following for all n in N : 2^(3n)-1 is divisible by 7 .

MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Prove that the Principle of Mathematical Induction does not apply to t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

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

    Text Solution

    |

  9. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  10. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

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

    Text Solution

    |

  12. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  17. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  18. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  19. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

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

    Text Solution

    |