If $\lim_{n \rightarrow \infty}\frac{1 - (10)^{n}}{1 + (10)^{n + 1}} = \frac{- \alpha}{10}$, then the value of $\alpha$ is

Question

Dr. Abubacker · Accepted Answer

(c)
$\lim_{n \rightarrow \infty}\frac{1 - (10)^{n}}{1 + (10)^{n + 1}}$
$= \lim_{n \rightarrow \infty}{\frac{10^{n}}{10^{n + 1}}\ \left( \frac{\frac{1}{10^{n}} - 1}{\frac{1}{10^{n + 1}} + 1} \right)}$
$\Rightarrow \ \ \ \ \ \ \ \  - \frac{\alpha}{10} = \frac{1}{10}\left( \frac{0 - 1}{0 + 1} \right) = - \frac{1}{10}$ [given]
$\Rightarrow \ \ \ \ \ \ \ \ \alpha = 1$

Q. If $\lim_{n \rightarrow \infty}\frac{1 - (10)^{n}}{1 + (10)^{n + 1}} = \frac{- \alpha}{10}$, then the value of $\alpha$ is

Explanation

Reviewed by Dr. Abubacker

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