Question

If $n$ is an integer, compute the value of the fraction \[ \frac{(1 + \theta)^n}{(1 - \theta)^{n-2}} \]

• A. $2i$
• B. $(2i)^n$
• C. $2r^{n-1}$
• D. $2r^{n-2}$

Hint:

For such fractional expressions, simplifying the powers of $\theta$ and recognizing patterns can help in directly evaluating the expression.

Answer 1

The Correct Option is A

By direct computation, we expand the terms based on the binomial expansion and simplify to find that the correct value for the fraction is $2i$ when $n$ is an integer.