Question

Find the value of $\underset{n\to \infty }{lim}\frac{a^n+b^n}{a^n+d^n},a>b,d$

• A. $-1$
• B. $1$
• C. $0$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$1$

${lim}_{n\to \infty }\frac{a^n+b^n}{a^n+d^n}$
$={lim}_{n\to \infty }\frac{1+{\left(\frac{b}{a}\right)}^n}{1+{\left(\frac{d}{a}\right)}^n}$
$=\frac{1+0}{1+0}$
$[\because {\left(\frac{b}{a}\right)}^n\to 0\text{and}{\left(\frac{d}{a}\right)}^n\to 0\text{as}n\to \infty ]$
$=1$