Question

Use induction to prove the following:
3^n > 2^n for all positive integers

Answer 1

I have a base case of 1 making 3^1>2^1 true and have n=k, making 3^k>2^k also true. n=k+1 seems like it would be a simple plug in, but I feel like I'm missing something

Answer 2

3^k > 2^k

multiply 3 both sides

3^(k+1) > 3*2^k
> 2*2^k
> 2^(k+1)

QED

Answer 3

Where does the three go on the right side?

Answer 4

\[\large a \gt 3 \implies a \gt 2\]

Answer 5

\[\large a \gt 3*2^k \implies a \gt 2*2^k\]

Answer 6

Okay that make more sense. Thanks!

Answer 7

yw!