Prove by Induction: 3n-1 is Divisible by 2

[BloodyFrozen]

I was doing this for practice and came across this problem-- I have no clue how to prove it.

By Induction, prove that 3ⁿ-1 is divisible by 2.

1) 3-1=2, divisible by two; good so far

Now I have no clue how to approach this.

Please help. Thanks in advance

 

[micromass]

Hi BloodyFrozen!

So, the induction hypothesis says that

$$3^n=2a+1$$

for some a. Now, try substitute this in $3^{n+1}-1$.

 

[BloodyFrozen]

Hi BloodyFrozen!

So, the induction hypothesis says that

$$3^n=2a+1$$

for some a. Now, try substitute this in $3^{n+1}-1$.

What do you mean sustituting it in?

 

[micromass]

What do you mean sustituting it in?

$$3^{n+1}-1=3.3^n-1=3.(2a+1)-1$$

 

[BloodyFrozen]

$$3^{n+1}-1=3.3^n-1=3.(2a+1)-1$$

Ok.
6a+2=2(3a+1).

Since this is multiplied by 2, it must be divisible by 2.
Thanks again (if you know what I mean ;P) micromass!