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  4. lim limitsn→∞ (an +bn/an - bn) where a > b > 1, is equal to

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

BITSATBITSAT 2016

Solution:

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