If `n>1` then `((2n)!)/(n!)^2`

If n is a positive integer, prove that 1-2n +(2n(2n-1))/(2!) - (2n(2n-1) (2n-2))/(3!) +… + (-1)^(n-1) (2n(2n-1) …(n+2))/((n-1)!) = (-1)^(n+1) ((2n)!)/(2(n!)^(2))

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer,prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)+...+(-1)^(n-1)(2n(2n-1)...(n+2))/((n-1)!)=(-1)^(n+1)(2n)!/2(n!)^(2)

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)+.......+(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)= (-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)= (-1)^(n+1)(2n)!//2(n !)^2dot

Prove that C_(0)-(1)/(3)*C_(1)+(1)/(5)*C_(2) - …+(-1)^(n)*(1)/(2n+1)C_(n) =(2^(2n)(n !)^(2))/((2n+1)!)

For all values of n. n ( n^(2) - 1) ( n^(2) - 4) ( n^(2) - 9)(n^(2) -16) (n^(2) -25) is divisible by