- #1

- 6

- 0

## Homework Statement

Prove that 3^n >= 2n+1 for all natural numbers.

## Homework Equations

3^n >= 2n+1 [is bigger or equal to]

## The Attempt at a Solution

3*1>=2+1

True for n=1

Assumption: 3^k>=2k+1

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

3^k*3>=2k+3

(2k+1)*3>=2k+3 <---can I just substitute 2k+1 into 3^k as per my assumption, because 3^k is bigger, and (2k+1)*3 is bigger than 2k+3? If so, is the proof complete?

Thanks in advance.