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How to find alternating series error bound

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10.10Alternating Series Error Bound

And the “structure” in the partial sum & remainder is: With a little twist, we will get the whole idea: ( Since the Rn is the gap between S & Sn, so

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The alternating series estimation theorem to

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Finding an Error Bound of a Taylor Polynomial Approximation

!To find the alternating series error bound, first find the error bound of the corresponding convergent series. Next, use the alternating series test to determine whether


Error Estimation of Alternating Series

Example Problem 1 - Finding an Error Bound of a Taylor Polynomial Approximation Using the Alternating Series Error Bound Step 1: . Find the Taylor expansion {eq}\sum_ {n=0}^\infty a_n
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Alternating Series Error Approximation

1 For an alternating series ∑ ( − 1) k a k, ( a k) k positive, monotonously falling to zero, the Leibniz test also provides an error bound. For s n the error bound is the next term a n

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