Could someone please help me with these questions? I just need to prove that n=K+1 using the assumption n=k

1) 1/(x-1) - 1/x - 1/x^2 - 1/x^3 -...-1/x^n = 1/[x^n(x-1)] for n=1,2,3...

2) 1+2x2+3x2^2 +...+nx2^(n-1) = 1 + (n-1)2^n for n=1,2,3...

3) 1.2+2^2.2^2+3^2.2^3+...+n^2.2^n = (n^2 -2n+3)2^(n+1) - 6

for n =1,2,3...

Thankyou ! =)