`((n+2)!-(n+1)!)/(n!)=`

Prove that ""^(2n+1)P_(n-1)=((2n+1)!)/((n+2)!) and ""^(2n-1)P_n=((2n-1)!)/((n-1)!)

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

1 ^(2) + 2^(2) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)

(2^(n)+2^(n-1))/(2^(n+1)-2^(n))

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 A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])