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

Prove the following by the principle of mathematical induction:`\ 7^(2n)+2^(3n-3). 3^(n-1)` is divisible 25 for all `n in Ndot`

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: \ x^(2n-1)+y^(2n-1) is divisible by x+y for all n in NNdot

Prove the following by the principle of mathematical induction: \ 2. 7^n+3. 5^n-5 is divisible 24 for all n in Ndot

Prove the following by the principle of mathematical induction: \ 11^(n+2)+12^(2n+1) is divisible 133 for all n in Ndot

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: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

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

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

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: \ 5^(2n)-1 is divisible by 24 for all n in Ndot

Prove the following by the principle of mathematical induction: 3^(2n)+7 is divisible by 8 for all n in Ndot

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. State First principle of mathematical induction

    Text Solution

    |

  20. Write the set of values of n for which the statement P(n):2n < n! is t...

    Text Solution

    |