First slide

Geometric progression

Question

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

Moderate

A

$|x| > 5$
B

$- 5 < x < 5$
C

$|x| < 5 / 2$
D

$|x| > 5 / 2$

Solution

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

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