Question

$\underset{n\to \infty }{lim}\frac{x^n+y^n}{x^n-y^n}$, where $x>y>0$ is equal to

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

Answer 1

The correct option is C 1

$\underset{n\to \infty }{lim}\frac{x^n+y^n}{x^n-y^n}$
$=\underset{n\to \infty }{lim}\frac{1+{\left(\frac{y}{x}\right)}^n}{1-{\left(\frac{y}{x}\right)}^n}$
$=\frac{1+0}{1-0}$ [As $x>y>0\Rightarrow \frac{y}{x}$ $<1$ $\Rightarrow .{\left(\frac{y}{x}\right)}^n$ $\to 0$ when $n\to \infty$. ]
$=1$.