Home
Class 11
MATHS
Show that 9^(n+1)-8n-9 is divisible by 6...

Show that `9^(n+1)-8n-9` is divisible by 64, where `n` is a positive integer.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

Write down the binomial expansion of (1+x)^(n+1) , when x=8. Deduce that 9^(n+1)-8n-9 is divisible by 64 where, n is a positive integer.

By using binomial theorem prove that (2^(3n)-7n-1) is divisible by 49 where n is a positive integer.

9^(n)-8^(n)-1 is divisible by 64 is

Show that 7^(n) +5 is divisible by 6, where n is a positive integer

Using binomial theorem show that 3^(4n+1)+16n-3 is divisible by 256 if n is a positive integer.

The statement : x^(n)-y^(n) is divisible by (x-y) where n is a positive integer is

(-i)^(4n+3) , where n Is a positive integer.

Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, where n is any positive integer.

Show that one and only one out of n ,n+2 or n+4 is divisible by 3, where n is any positive integer.

Show that n^2-1 is divisible by 8, if n is an odd positive integer.

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Show that no three consecutive binomial coefficients can be in G.P.

    Text Solution

    |

  2. Find the sum sum(r=1)^n r^n (^nCr)/(^nC(r-1)) .

    Text Solution

    |

  3. Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integ...

    Text Solution

    |

  4. If the 3rd, 4th , 5th and 6th term in the expansion of (x+alpha)^n ...

    Text Solution

    |

  5. Find the remainder when 7^(98) is divided by 5.

    Text Solution

    |

  6. Show that 2^(4n+4)-15n-16, where n in N is divisible by 225.

    Text Solution

    |

  7. If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0lt f lt...

    Text Solution

    |

  8. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

    Text Solution

    |

  9. If 9^7+7^9 is divisible b 2^n , then find the greatest value of n ,w...

    Text Solution

    |

  10. Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even ...

    Text Solution

    |

  11. Find the remainder when x=5^(5^(5^(5...))) (24 times 5) is divided by ...

    Text Solution

    |

  12. Find the remainder when 1690^(2608)+2608^(1690) is divided by 7.

    Text Solution

    |

  13. Find the value of {3^(2003)//28}, w h e r e{dot} denotes the fractiona...

    Text Solution

    |

  14. Find the remainder when 5^(99) is divided by 13.

    Text Solution

    |

  15. Find the remainder when 7^(103) is divided by 25.

    Text Solution

    |

  16. Using binomial theorem, prove that 6^n-5n always leaves remainder 1...

    Text Solution

    |

  17. If the coefficient of the middle term in the expansion of (1+x)^(2n+2)...

    Text Solution

    |

  18. If the coefficients of three consecutive terms in the expansion of (1+...

    Text Solution

    |

  19. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

    Text Solution

    |

  20. Prove that (C0+C1)(C1+C2)(C2+C3)(C3+C4)...........(C(n-1)+Cn) = (C0...

    Text Solution

    |