Home
Class 11
MATHS
Prove that: ((2n)!)/(n !)={1. 3. 5 (2n-1...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    RD SHARMA ENGLISH|Exercise All Questions|86 Videos

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|290 Videos

Similar Questions

Explore conceptually related problems

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

Prove that: \ ^(2n)C_n=(2^n[1. 3. 5 (2n-1)])/(n !)

Prove that : 1+2+3++n=(n(n+1))/2

Prove that (^(2n)C_0)^2-(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot

Prove that: (1+1/1)(1+1/2)(1+1/3)(1+1/n)=(n+1) for all n in Ndot

Prove that .^n C_0 . ^(2n) C_n- ^n C_1 . ^(2n-2)C_n+^n C_2 . ^(2n-4)C_n-=2^ndot

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

Prove that (1)/(1!(n-1)!) + (1)/(3!(n-3)!)+ (1)/(5!(n-5)!) + …….= (2^(n-1))/(n!)

Prove that log_e ((n^2)/(n^2-1))=1/(n^2)+1/(2n^4)+1/(3n^6)+........oo

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))

RD SHARMA ENGLISH-PERMUTATIONS-All Questions
  1. Find the number of arrangements of the letters of the MISS.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Find n , if (n+2)! =2550xxn !

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that: n(n-1)(n-2)....(n-r+1)=(n !)/((n-r)!)

    Text Solution

    |

  8. If w(1).w(2),w(3) and w(4) are work done in isothermal, adiabatic, iso...

    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 arrange...

    Text Solution

    |

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

    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 5 letters words can be formed using the letters of the words ...

    Text Solution

    |

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

    Text Solution

    |

  19. A gentle man wants to invite six friends. In how many ways he can send...

    Text Solution

    |

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

    Text Solution

    |