Home
Class 11
MATHS
Prove the following by using the princip...

Prove the following by using the principle of mathematical induction for all `n in N`:`n(n + 1) (n + 5)`is a multiple of 3.

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

Prove the following by using the principle of mathematical induction for all n in N : 41^n-14^n is a multiple of 27.

Using principle of mathematical induction, prove that for all n in N, n(n+1)(n+5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N : 10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N : 3^(2n+2)-8n-9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n in N : x^(2n)-y^(2n) is divisible by x + y .

Prove the following by using the principle of mathematical induction for all n in N : 1 + 2 + 3 + ... + n <1/8(2n+1)^2 .

Prove the following by the principle of mathematical induction: \ (a b)^n=a^n b^n for all n in Ndot

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

Using the principle of mathematical induction, prove that n<2^n for all n in N

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Prove the following by the principle of mathematical induction:\ 7^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Prove the following by the principle of mathematical induction: n^3...

    Text Solution

    |

  8. Prove the following by the principle of mathematical induction:\ 1+2...

    Text Solution

    |

  9. Prove the following by the principle of mathematical induction: 7+77...

    Text Solution

    |

  10. Prove the following by the principle of mathematical induction: (n^7...

    Text Solution

    |

  11. Prove the following by the principle of mathematical induction:(n^(1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Prove the following by the principle of mathematical induction: ((2...

    Text Solution

    |

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

    Text Solution

    |

  16. Prove that: \ sin x+sin3x++sin(2n-1)x=(sin^2\ \ n x)/(sin x) for all n...

    Text Solution

    |

  17. Given a1=1/2(a0+A/(a0)), a2=1/2(a1+A/(a1)) and a(n+1)=1/2(an+A/(an)) ...

    Text Solution

    |

  18. Let P(n) be the statement: 2^n >= 3n. If P(r) is true, show that P (r...

    Text Solution

    |

  19. The distributive law from algebra states that for all real numbers c,a...

    Text Solution

    |

  20. State First principle of mathematical induction

    Text Solution

    |