Question

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

• A. |x|>5
• B. -5<x<5
• C. |x|<5/2
• D. |x|>5/2

Answer 1

The correct option is A

|x|>5

We can rewrite the series as

1 + 1 + $\frac{5}{x}$ + ${\left(\frac{5}{x}\right)}^2$ + ${\left(\frac{5}{x}\right)}^3$ + ........

We can sum up this series if | $\frac{5}{x}$| < 1

⇔ |x| > 5