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**[SOLVED] radius of convergence**

## Homework Statement

Let D be th region in the xy plane in which the series

[tex]\sum_{k=1}^{\infty}\frac{(x+2y)^k}{k}[/tex]

converges. Describe D.

## Homework Equations

## The Attempt at a Solution

By the ratio test, we find the radius of converge of the series in x+ 2y to be 1. So, the series will converge when |x+2y| < 1. This region is a rectangle.

What is wrong with this?