Question

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

• A. $\mid x\mid >5$
• B. -5 < x < 5
• C. $\mid x\mid <5/2$
• D. $\mid x\mid >5/2$

Answer 1

Answer: (A)

$\mid x\mid >5$

We can rewrite the series as
$1+1+\frac{5}{x}+(\frac{5}{x}{)}^2+(\frac{5}{x}{)}^3+.....$
We can sum up this series if $\mid 5/x\mid <1$
$\iff \mid x\mid >5$