Question

$\underset{n\to \infty }{lim}\frac{a^n+b^n}{a^n-b^n}$, where $1<b<a$, is equal to

• A. -1
• B. 1
• C. 0
• D. none of these

Answer 1

The correct option is B 1

We have 1 < b < a.
$\therefore 0<\frac{b}{a}<1\Rightarrow \underset{n\to \infty }{lim}{\left(\frac{b}{a}\right)}^n=0$
So, $\underset{n\to \infty }{lim}\frac{a^n+b^n}{a^n-b^n}=\underset{n\to \infty }{lim}\frac{1+{\left(\frac{b}{a}\right)}^n}{1-{\left(\frac{b}{a}\right)}^n}=\frac{1+0}{1-0}=1$