Home
Class 11
MATHS
Prove that (n !+1) is not divisible by ...

Prove that `(n !+1)` is not divisible by any natural number between `2` and `n`

Text Solution

Verified by Experts

Since n! = 1 . 2 . 3 . 4 ..... (n – 1) . n
Therefore n! is divisible by any number from 2 to 'n'.
Consequently n! + 1, when divided by any number between 2 and 'n' leaves 1 as remainder.
Hence, n! + 1 is not divisible by any number between 2 and 'n'.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    RD SHARMA|Exercise Solved Examples And Exercises|81 Videos

  • PROBABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|280 Videos

Similar Questions

Explore conceptually related problems

prove that 4^(n)-1 is divisible by 3, for each natural number n.

prove that 3^(2n)-1 is divisible by 8, for all natural numbers n.

prove that n(n^(2)+5) is divisible by 6, for each natural number n.

Prove that (n!)! is divisible by (n!)^((n-1)!)

Show that 10^(2n-1)+1 is divisible by 11 for all natural numbers n.

n^(3)-n is divisible by 6, for each natural numbers n ge2

When n!+1 is divided by any natural number obtained is between 2 and n then remainder is

If n is any natural number, then 5^(2n)-1 is always divisible by how many natural numbers ?

There are _________ natural numbers between n^2 and (n + 1)^2

RD SHARMA-PERMUTATIONS-Solved Examples And Exercises
  1. Prove that 33! is divisible by " 2^15. what is the largest integer n s...

    Text Solution

    |

  2. Prove that (n !)^2 < n^n n! < (2n)!, for all positive integers n.

    Text Solution

    |

  3. Prove that (n !+1) is not divisible by any natural number between 2 a...

    Text Solution

    |

  4. Prove that: ((2n)!)/(n !)={1. 3. 5 (2n-1)}2^ndot

    Text Solution

    |

  5. If (n !)/(2!(n-2)!) and (n !)/(4!(n-4)!) are in the ratio 2:1 , find t...

    Text Solution

    |

  6. Find n , if (n+2)! =2550xxn ! (ii) (n+1)! =12xx(n-1)!

    Text Solution

    |

  7. If 1/(9!)+1/(10 !)=x/(11 !) , find xdot

    Text Solution

    |

  8. If ((2n)!)/(3!(2n-3)!)a n d(n !)/(2!(n-2)!) are in the ratio 44 :3, fi...

    Text Solution

    |

  9. How many permutations of the letters of the word MADHUBANI do not b...

    Text Solution

    |

  10. Find the probability that in a random arrangement of the letters of th...

    Text Solution

    |

  11. How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so ...

    Text Solution

    |

  12. If the letters of the word ‘MOTHER’ are written in all possible orders...

    Text Solution

    |

  13. In how many ways can the letters of the word PERMUTATIONS be arrang...

    Text Solution

    |

  14. In how many ways can the letters of the word PERMUTATIONS be arrange...

    Text Solution

    |

  15. (i) How many different words can be formed with letters of the word ‘S...

    Text Solution

    |

  16. How many words can be formed using the letter A thrice, the letter B ...

    Text Solution

    |

  17. How many 4 letters words can be formed using the letters of the words ...

    Text Solution

    |

  18. m men and n women are to be seated in a row so that no two ...

    Text Solution

    |

  19. A gentle man want to invite six friends. In how many ways and he se...

    Text Solution

    |

  20. How many three-digit numbers more than 600 can be formed by using the ...

    Text Solution

    |