Home
Class 11
MATHS
Prove that for n in N ,10^n+3. 4^(n+2)+...

Prove that for `n in N ,10^n+3. 4^(n+2)+5` is divisible by `9` .

Text Solution

Verified by Experts

Given,`10^n+3.4^(n+2)+5 `
Put n=1
`10+3(64)+5=207 `which is divisible by `3,9,23,207`
We will check for n=2
`100+768+5=873 ` which is divisible by 3 and 9 only.
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA|Exercise Solved Examples And Exercises|181 Videos

Similar Questions

Explore conceptually related problems

Prove by using the principle of mathematical induction that for all n in N, 10^(n)+3.4^(n+2)+5 is divisible by 9

Using the principle of Mathematical Induction, prove that forall nin N , 4^(n) - 3n - 1 is divisible by 9.

If n in N , then 3^(2n)+7 is divisible by

For all n in N , 4^(n)-3n-1 is divisible by

10^n+3(4^(n+2))+5 is divisible by (n in N)

n^(3)+2n divisible by

10^(n)+3(4)^(n+2)+5,n in N is divisible by 9

Prove that for any natural numbers n, 7^(n)-2^(n) is divisible by 5.

Knowledge Check

  • 3^(2n+2)-8n-9 is divisible by

    A
    36
    B
    49
    C
    64
    D
    none

  • If n in N , then 3^(2n)+7 is divisible by

    A
    3
    B
    8
    C
    9
    D
    11

  • For all n in N , 4^(n)-3n-1 is divisible by

    A
    3
    B
    8
    C
    9
    D
    11
    • RD SHARMA-MATHEMATICAL INDUCTION-Solved Examples And Exercises
    1. Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

      Text Solution

      |

    2. Prove by induction that the sum of the cubes of three consecutive n...

      Text Solution

      |

    3. A sequence x1, x2, x3,.... is defined by letting x1=2 and xk=x(k-1)...

      Text Solution

      |

    4. Show by the Principle of Mathematical induction that the sum Sn, of th...

      Text Solution

      |

    5. Using the principle of mathematical induction prove that : 1. 3+2. ...

      Text Solution

      |

    6. Prove by the principle of mathematical induction that for all n in N ...

      Text Solution

      |

    7. Using the principle of mathematical induction prove that 1+1/(1+2)...

      Text Solution

      |

    8. Prove by induction that the sum Sn=n^3+2n^2+5n+3 is divisible by 3 for...

      Text Solution

      |

    9. Using the principle of mathematical induction prove that 1/(1. 2. ...

      Text Solution

      |

    10. Using the principle of mathematical induction. Prove that (x^(n)-y^(n...

      Text Solution

      |

    11. Using the principle of mathematical induction prove that 41^n-14^n ...

      Text Solution

      |

    12. Using the principle of mathematical induction, prove that (2^(3n)-1) i...

      Text Solution

      |

    13. Using principle of mathematical induction prove that sqrtn<1/sqrt1+1/s...

      Text Solution

      |

    14. Prove that: 1+2+3+ n<((2n+1)^2)/8 for all""n in Ndot

      Text Solution

      |

    15. Prove that 1^2+2^2+dotdotdot+n^2>(n^2)/3,n in N

      Text Solution

      |

    16. Prove by the principle of mathematical induction that n<2^n"for all"n ...

      Text Solution

      |

    17. Prove by the principle of mathematical induction that for all n in N ...

      Text Solution

      |

    18. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

      Text Solution

      |

    19. Prove the following by using the principle of mathematical inductio...

      Text Solution

      |

    20. Using principle of MI prove that 2.7^n+3.5^n-5 is divisible by 24

      Text Solution

      |