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

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

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

Similar Questions

Explore conceptually related problems

n^2-1 is divisible by 8, if n is

Show that n^7-n is divisible by 42 .

If p is a natural number, then prove that p^(n+1) + (p+1)^(2n-1) is divisible by p^(2) + p +1 for every positive integer n.

If a and b are distinct integers, prove that a - b is a factor of a^(n) - b^(n) ,whenever n is a positive integer.

If a and b are distinct integers, prove that a- b is a factor of a^n -b^n , whenever n is a positive integer. [Hint write a^n = (a - b + b)^n and expand]

Using Permutation or otherwise, prove that ((n^2)!)/((n!)^2) is an integer, where n is a positive integer.

Prove that the function f(x) = x^n , is continuous at x=n , where n is a positive integer.

MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

    Text Solution

    |

  2. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

    Text Solution

    |

  3. Show that 9^(n+1) - 8n -9 is divisible by 64, whenever n is a positiv...

    Text Solution

    |

  4. Using Binomial theorem, prove that 6^(n)-5n always leaves remainder 1...

    Text Solution

    |

  5. Evaluate the following : ""^12C0+""^12C1+""^12C2+ ....... +""^12C12.

    Text Solution

    |

  6. Evaluate the following : ""^12C0+""^12C2+""^12C4 +""^12C12.

    Text Solution

    |

  7. Evaluate the following : ""^16C1+""^16C3+""^16C5+ ....... +""^16C15.

    Text Solution

    |

  8. Prove that underset (r=0) overset (n) sum 3^r ""^nCr =4^n.

    Text Solution

    |

  9. Prove that ""^nC0+3""^nC1+5""^nC2+........+(2n+1)""^nCn= (n+1)2^n.

    Text Solution

    |

  10. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

    Text Solution

    |

  11. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : (1+...

    Text Solution

    |

  12. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

    Text Solution

    |

  13. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0+...

    Text Solution

    |

  14. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : 2C0...

    Text Solution

    |

  15. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : 2C0...

    Text Solution

    |

  16. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0C...

    Text Solution

    |

  17. Prove that C0Cr+C1 C(r+1)+ C2 C(r+2)+...............+c(n-r) Cn=((2n)!...

    Text Solution

    |

  18. Find the coefficient of x^(n-r) in the expansion of (x+1)^n (1+x)^n. ...

    Text Solution

    |

  19. Find the coefficient of x^4 in the expansion of (1+x)^n (1-x)^n. Deduc...

    Text Solution

    |

  20. Write and simplify the term involving a^2b^5 in (a-2b)^4 (a+b)^3.

    Text Solution

    |