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

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

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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

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

Prove that ((n + 1)/(2))^(n) gt n!

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Prove that [(n+1)//2]^n >(n !)dot

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

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" +(. ^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1) .

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))