Hello everyone!

to start with I am new to this forum and I come from sweden so I am not that good in english mathematic terms. But I will try my best. Also I am going in highschool and not college/university but sinse the course I am taking is named "Descrete mathe" I thought it would fit quiet good here. Anyway, I think this is very easy but I am in year 1 in highschool so for me it's hard.

I need to prove thatn= 1,2,3 ...

is working for

a) 2 + 4 +...+ 2n=n(n+1)

b) 1 + 2 + 4 +...+ 2^n= 2^(n+1)-1

I cant even figure out the A..

This is how I do it, please help me !

n=1 VL=2, HL=1(1+1)=2, VL=HL

n=p,

2 + 4 +...+ 2p = p(p+1)

n=p+1,

2 + 4 +...+ 2p + (2p+1) = (p+1)(p+2)

p(p+1)+(2p+1) = (p+1)(p+2)

p^2+p+2p+1= p^2+p+2p+2

Now why is that wrong, I am doing something wrong..