Find the value of x so that the series below converges

Question

Find the value of x so that the series below converges 

infinity Σ n=1 (xⁿ/10ⁿ) 

 

What is the answer in interval notation?

Answer 1

This is the same as ∑ (x/10)ⁿ, which is a geometric series.

 

A geometric series converges if the absolute value of the ratio between each number in the series is less than 1.  So what you need here is for |x/10| < 1, or |x| < 10.

 

In interval notation, this would be (-10, 10).