If the sum of the series 2+5x+25×2+125×3+… is finite, then

# If the sum of the series $2+\frac{5}{x}+\frac{25}{{x}^{2}}+\frac{125}{{x}^{3}}+\dots$ is finite, then

1. A

$\left|x\right|>5$

2. B

$-5

3. C

$\left|x\right|<5/2$

4. D

$\left|x\right|>5/2$

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### Solution:

We can rewrite the series as
$1+1+\frac{5}{x}+{\left(\frac{5}{x}\right)}^{2}+{\left(\frac{5}{x}\right)}^{3}+\dots$
We can sum up this series if $\left|\frac{5}{x}\right|<1⇔|x|>5$

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