Home
Class 11
MATHS
Prove that : (2n) ! = 2^n (n!)[1.3.5.......

Prove that : `(2n) ! = 2^n (n!)[1.3.5.... (2n-1)]` for all natural numbers n.

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    MODERN PUBLICATION|Exercise EXERCISE|319 Videos

  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise EXERCISE|169 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|348 Videos

Similar Questions

Explore conceptually related problems

Prove that : ^(2n)C_n = (2^n [1.3.5. ..........(2n-1)])/(n!) .

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

Prove that : "^nP_n= 2^nP_(n-2) .

Prove that n! + (n + 1)! = n! (n + 2)

Prove that n! (n+2)=n!+(n+1)! .

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

Prove that log_n(n+1)>log_(n+1)(n+2) for any natural number n > 1.

Prove that i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 , for all n in N .

Prove that : 7^(2n)+(2^(3n-3))(3^(n-1)) is divisible by 25 forall n in N .

By the Principle of Mathematical Induction, prove the following for all n in N : 1+3+5+....... +(2n-1) =n^2 i.e. the sum of first » odd natural numbers is n^2 .