How do you use math induction to prove 3^n > 2n ?

Question

Thank you!

Answer 1

for n = 0
3^0 = 1
2*0 = 0 so true

for n=1
3^1 = 3
2n = 2 so true

for further n
3^(n+1) = 3 * 3^n
2(n+1) = 2 + 2n
for any n bigger than 1 is 3^n > 2 n ??

n = 2
9 > 4
n=3
27 > 6
n =4
81 > 8
see what is happening?

Answer 2

They all worked?
But I don't get the fuurther n part...
for further n
3^(n+1) = 3 * 3^n ( why 3 is multiplied by 3^n)
2(n+1) = 2 + 2n (why is 2 added to3 ^n)

Thank you!

Answer 3

I mean why is 2 added to 2n...?

Answer 4

Oh, I think I got it now