" 6.Prove that "2,6.10.14..." to "n" factors "=((2n)!)/(n!)=(n+1)(n+2)..." to "n" factors."

Show that 2.6.10……. to n factors =((2n)!)/(n!)

Show that 2.6.10.14.. To n factors =(n+1)(n+2)(n+3) … to n factors.

the continued product 2.6.10.14... to n factors is equal to 2np_(n)(b)^(2n)C_(n)(n+1)(n+2)(n+3)...(n+n)2^(n)*(1.3.5......2n-1)

Prove that ((2n)!) / (n!) = 2^n(2n - 1) (2n - 3) ... 5.3.1.

By method of induction, prove that 1.6 + 2.9 + 3.12 +... +to n terms = n(n +1 )(n+2) for all n in N .

Prove that 2 + 4 + 6 + .... + 2n = n (n + 1)

Factor n^(2)-5n-14 .

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

Prove that ((2n+1)!)/(n!)=2^(n){1.3.5(2n-1)(2n+1)}

Prove that (1)/(n!)+(1)/(2!(n-2)!)+(1)/(4!(n-4)!)+...=(1)/(n!)2^(n-1)