Question

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

• A. -1
• B. 1
• C. 0
• D. None

Answer 1

Answer: (B)

$\text{limit}={\lim }_{n\to \infty }\frac{1+{\left(\frac{b}{a}\right)}^n}{1-{\left(\frac{b}{a}\right)}^n}=1,$
because $0<\frac{b}{a}<1$ implies ${\left(\frac{b}{a}\right)}^n\to 0$ as $n\to \infty$