Find the radius of convergence and interval of convergence.
- Thread starter Aramid
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LCKurtz
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It's very hard to read your image but I think you have it down to something like this:
[MATH]\frac{n^3 + O(n^2)}{n^3 + O(n^2)}\frac{|x|} 4[/MATH], where [MATH]O(n^2)[/MATH] means terms of degree [MATH]2[/MATH] or less in [MATH]n[/MATH].
You almost have it. Take your fraction of cubic polynomials and divide both numerator and denominator by [MATH]n^3[/MATH]. Then look at what happens as [MATH]n\to \infty[/MATH]. Notice that you need absolute values around the [MATH]x[/MATH]. What values of [MATH]x[/MATH] make the limit less than [MATH]1[/MATH]?
[MATH]\frac{n^3 + O(n^2)}{n^3 + O(n^2)}\frac{|x|} 4[/MATH], where [MATH]O(n^2)[/MATH] means terms of degree [MATH]2[/MATH] or less in [MATH]n[/MATH].
You almost have it. Take your fraction of cubic polynomials and divide both numerator and denominator by [MATH]n^3[/MATH]. Then look at what happens as [MATH]n\to \infty[/MATH]. Notice that you need absolute values around the [MATH]x[/MATH]. What values of [MATH]x[/MATH] make the limit less than [MATH]1[/MATH]?