Induction questions HELP

[halukbach]

I have some induction questions which I don't know how to solve. Can you solve ? Thank you :)

1-Prove that 7^8n+3 + 2 , is divisible by 5


2- Consider z=r(cos@ +isin@)
Prove that z^n= r^n (cos n@+isin n@)

3- Prove that 1+2(1/2) + 3(1/2)^2 + 4(1/2)^3+.... + n(1/2)^n-1 = 4- (n+2 / 2^n-1)