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

Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

The sum of the series 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n-1)!1!) is = (A) 1/(n!2^n) (B) 2^n/n! (C) 2^(n-1)/n! (D) 1/(n!2^(n-1)

Using the principle of mathematical induction , prove that for n in N , (1)/(n+1) + (1)/(n+2) + (1)/(n+3) + "……." + (1)/(3n+1) gt 1 .

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

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

Prove that (n-1)^(2) C_(1) + (n-3)^(2) C_(3) + (n-5)^(2) C_(5) . + ….= n (n+1)2^(n-3) , where C_(r) stands for ""^(n)C_(r) .

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

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 (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .