Home
Class 11
MATHS
Show that 1!+2!+3!++n ! cannot be a perf...

Show that `1!+2!+3!++n !` cannot be a perfect square for any `n in N ,ngeq4.`

Promotional Banner

Topper's Solved these Questions

  • LOGARITHM

    CENGAGE ENGLISH|Exercise All Questions|173 Videos

  • PROBABILITY

    CENGAGE ENGLISH|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Show that 12^n cannot end with the digits 0 or 5 for any natural number n

Show that: 2^(4n)-2^n(7n+1) is some multiple of the square of 14, where n is a positive integer.

Prove that sqrt(n) is not a rational number. if n is not a perfect square.

Prove that sqrt(n) is not a rational number. if n is not a perfect square.

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

A perfect square is a positive integer that is the result of squaring a positive integer. If N = 3^4 cdot 5^3 cdot 7, then what is the biggest perfect square that is a factor of N?

n is a natural number. It is given that (n +20) + (n +21) + ......+ (n + 100) is a perfect square. Then the least value of n is "___________"

If (2^(200)-2^(192).31+2^n) is the perfect square of a natural number , then find the sum of digits of 'n' .

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

CENGAGE ENGLISH-PERMUTATIONS AND COMBINATIONS-All Questions
  1. Find the number of ways in which the number 94864 can be resolved as a...

    Text Solution

    |

  2. A class contains three girls and four boys. Every Saturday, five go...

    Text Solution

    |

  3. Show that 1!+2!+3!++n ! cannot be a perfect square for any n in N ,ng...

    Text Solution

    |

  4. If all the words formed from the letters of the word HORROR are arra...

    Text Solution

    |

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

    Text Solution

    |

  6. A person always prefers to eat parantha and vegetable dish in his m...

    Text Solution

    |

  7. The letters of word ZENITH are written in all possible ways. If all ...

    Text Solution

    |

  8. In a class tournament, all participants were to plan different game...

    Text Solution

    |

  9. How many words can be formed with the letters o the word MATHEMATICS b...

    Text Solution

    |

  10. There are 720 permutations of the digits 1, 2, 3, ,4 ,5, 6. Suppose th...

    Text Solution

    |

  11. Five different digits from the setoff numbers {1,2,3,4,5,6,7} are writ...

    Text Solution

    |

  12. A shelf contains 20 books of which 4 are single volume and the other ...

    Text Solution

    |

  13. How many different numbers of 4 digits can be formed from the digits 0...

    Text Solution

    |

  14. How many six-digit odd numbers, greater than 6,00,000, can be formed ...

    Text Solution

    |

  15. Eleven animals of a circus have to be placed in eleven cages (one in e...

    Text Solution

    |

  16. If A={x|x is prime number and x<30}, find the number of different rati...

    Text Solution

    |

  17. Find the sum of all the numbers that can be formed with the digits 2, ...

    Text Solution

    |

  18. How any 4-letters words, with or without meaning, can be formed out of...

    Text Solution

    |

  19. Find the numbers of positive integers from 1 to 1000, which are div...

    Text Solution

    |

  20. Find the number of ways in which two Americans, two British, one Ch...

    Text Solution

    |