- #1

Illania

- 26

- 0

## Homework Statement

Given [itex]x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+... = k[/itex], are there any values of x for the values [itex]k = -100, \frac{1}{2}, 100[/itex]?

## Homework Equations

## The Attempt at a Solution

I started by finding that the series is [itex]\Sigma^{\infty}_{n=1} \frac{(-1)^{n+1}x^n}{n} = k[/itex]. I then used the ratio test to find that the radius of convergence = R = 1. I'm not really sure where to go from here though. I'm hoping someone can point me in the right direction as to how I can begin to find out if there are any values of x so that the series equals either -100, [itex]\frac{1}{2}[/itex], or 100.