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Example 3: e

Approximate e-1 within 0.001. The power series for ex is

09_infinite_series-629.gif , r = ∞. Setting x = -1,

09_infinite_series-630.gif

The series alternates and the last term is less than 0.001, so

09_infinite_series-631.gif error ≤09_infinite_series-632.gif~ 0.0002.

Adding up,

e-1 ~ 0.36806, error ≤ 0.0002.

The actual value is e-1 ~ 0.36788.


Last Update: 2006-11-15