- #1
ehrenfest
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[SOLVED] rudin 8.10
Prove that [itex](1-x)^{-1} \leq \exp 2x[/tex] when [itex]0 \leq x \leq 1/2[/itex].
[tex]e^x = \sum_{i=0}^{\infty}\frac{x^n}{n!}[/tex]
[tex]1/(1-x) = 1+x+x^2+\cdots[/tex]
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.
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.