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**[SOLVED] rudin 8.10**

## Homework Statement

Prove that [itex](1-x)^{-1} \leq \exp 2x[/tex] when [itex]0 \leq x \leq 1/2[/itex].

## Homework Equations

[tex]e^x = \sum_{i=0}^{\infty}\frac{x^n}{n!}[/tex]

[tex]1/(1-x) = 1+x+x^2+\cdots[/tex]

## The Attempt at a Solution

I tried working with the series and that failed miserable. Maybe I need to use calculus and find out whether the function is increasing or decreasing but I started that but I tried that a little and did not see how it would help.