I am in dire need of assistance!!!

[Hiva]

 

[JeffM]

There are at least three ways to attack this problem.

The most general is to realize that

[math]4^n - 1 = (2^2)^n - 1 = 2^{2n} - 1.[/math]
Can you see the next step?

 

[Deleted member 4993]

View attachment 28416

Do you see that (4^n -1 ) is in the form of ( a^2 - b^2) ?

Do you know that:

(a^2 - b^2) = (a + b) * (a - b)

Use those "facts" to simplify the numerator and proceed.

 

[Harry_the_cat]

You could also use the fact that it is a multiple choice question to test out each answer. Remember that if \(\displaystyle \frac{a}{b}=c\) then \(\displaystyle a=b*c\).
So multiply the denominator by the expressions A-D to see which one gives you the numerator.