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  4. displaystyle lim n arrow ∞ (an+bn/an-bn), where 1<b<a, is equal to

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Q. $\displaystyle\lim _{n \rightarrow \infty} \frac{a^{n}+b^{n}}{a^{n}-b^{n}}$, where $1
Limits and Derivatives

Solution:

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