Home
Class 11
MATHS
Prove the following by the principle o...

Prove the following by the principle of mathematical induction: `1+3+5++(2n-1)=n^2i.e.` the sum of first `n` odd natural numbers is `n^2dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA ENGLISH|Exercise All Questions|182 Videos

Similar Questions

Explore conceptually related problems

Prove the following by the principle of mathematical induction: 1+3+3^2++3^(n-1)=(3^n-1)/2

Prove the following by the principle of mathematical induction: 1+2+3++n=(n(n+1))/2idote , the sum o the first n natural numbers is (n(n+1))/2dot

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by the principle of mathematical induction: \ 1^2+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)

Prove the following by the principle of mathematical induction: 1/2+1/4+1/8++1/(2^n)=1-1/(2^n)

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove the following by using the principle of mathematical induction for all n in N : (2n+7)<(n+3)^2 .

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

Prove the following by the principle of mathematical induction: \ 5^(2n)-1 is divisible by 24 for all n in Ndot

Prove the following by the principle of mathematical induction: \ 5^(2n+2)-24 n-25 is divisible 576 for all n

RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Prove the following by the principle of mathematical induction: 1+3...

    Text Solution

    |

  2. Using the principle of mathematical induction, prove that 1/(1*2)...

    Text Solution

    |

  3. Prove the following by the principle of mathematical induction: 1+3+...

    Text Solution

    |

  4. Prove the following by the principle of mathematical induction:1/(2...

    Text Solution

    |

  5. Prove the following by the principle of mathematical induction: 1/(1...

    Text Solution

    |

  6. Prove the following by the principle of mathematical induction: 1/(...

    Text Solution

    |

  7. Prove the following by the principle of mathematical induction: 1/(3...

    Text Solution

    |

  8. Prove the following by the principle of mathematical induction: \ 1...

    Text Solution

    |

  9. Prove the following by the principle of mathematical induction: 2+5...

    Text Solution

    |

  10. Prove the following by the principle of mathematical induction: \ 1....

    Text Solution

    |

  11. Prove the following by the principle of mathematical induction: \ 1...

    Text Solution

    |

  12. Prove the following by the principle of mathematical induction:1/2+...

    Text Solution

    |

  13. Prove the following by the principle of mathematical induction: \ 1...

    Text Solution

    |

  14. Prove the following by the principle of mathematical induction: a+(a...

    Text Solution

    |

  15. Prove the following by the principle of mathematical induction:\ 5^...

    Text Solution

    |

  16. Prove the following by the principle of mathematical induction: 3^(...

    Text Solution

    |

  17. Prove the following by the principle of mathematical induction:\ 5^(...

    Text Solution

    |

  18. Prove the following by the principle of mathematical induction:\ 3^...

    Text Solution

    |

  19. Prove the following by the principle of mathematical induction:\ (a...

    Text Solution

    |

  20. Prove the following by using the principle of mathematical induction ...

    Text Solution

    |