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Home Infinite Series Approximating Power Series Examples Example 2: arctan  
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Example 2: arctan
Approximate arctan ½ within 0.001. The power series for arctan x is r = 1. Setting x = ½, This an an alternating series. The last term is less than 0.001, Therefore error ≤ 0.0002. Adding up, arctan ½ ~ 0.4635, error ≤ 0.0002. The series r = 1 can be used to approximate π. We start with Setting x = 1/√3 in the series, or This is an alternating series, so , error ≤ ~ 0.9072, error ≤ 0.0004. Dividing everything by √3/6 we get π ~ 3.1426, error ≤ 0.0013.


Home Infinite Series Approximating Power Series Examples Example 2: arctan 