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Home Infinite Series Approximating Power Series Examples Example 1: ln  
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Example 1: ln
Approximate ln (1½) within 0.01. We use the power series for ln (1  x), , r = 1. Setting 1  x = 1½, x = ½, This is an alternating series. The last term shown is less than 0.01, 1/(5 · 32) = 1/160 ~ 0.006. By the Alternating Series Test, the error in each partial sum is less than the next term. So , error ≤ or ln (1½) ~ 0.401, error ≤ 0.006. The actual value is ln (1½) ~ 6.405.


Home Infinite Series Approximating Power Series Examples Example 1: ln 