What is the radius of convergence? Given a real power series + ∞ ∑ n=0an(x −x0)n, the radius of convergence is the quantity r = sup{˜r ∈ R: +∞ ∑ n=0an˜rn converges}. Note that r ≥ 0, because
Using the Ratio test, we can find the radius of convergence of given power series as explained below. Step 1: Let an = cn (x – a)n and an+1 = cn+1 (x – a)n+1 Step 2: Consider the limit for the absolute value of an+1/anas n → ∞. i.e., Step 3:Simplify the ratio Step 4:Finally compute the result for R based on the scenarios give See more
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Steps on How to Find the Radius of Convergence for a Power Series. Step 1: Compute the
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With this in mind, we can state the universal fact that, given an interval of convergence???a
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