Radius of Convergence
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From the Calculus II: Taylor & Maclaurin Series curriculum
<h2>Ratio Test Application</h2>
<p>Not all series converge for all x. To find the <b>Interval of Convergence</b>, we typically use the Ratio Test.</p>
<h3>The Logic:</h3>
<ol>
<li>Take the limit as n approaches infinity of |a_(n+1) / a_n|.</li>
<li>Set the result < 1 to find the values of x where it converges.</li>
<li><b>Check Endpoints:</b> Always plug the endpoints back into the original series to check for conditional convergence.</li>
</ol>
<p><b>Homework Help:</b> Use our <b>AI Math Solver</b> to check your ratio test steps if you keep getting 'Infinity'.</p>
Frequently asked about Radius of Convergence
Ratio Test Application Not all series converge for all x. To find the Interval of Convergence , we typically use the Ratio Test. The Logic: Take the limit as n approaches infinity of a(n+1) / an . Read the full notes above for the details.
Radius of Convergence is a core topic in Calculus II: Taylor & Maclaurin Series. Most exam papers test it via a mix of definitions, worked examples, and applied problems. The notes above cover the high-yield sub-topics, common pitfalls, and the kind of questions examiners typically set.
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