Example 3: e

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

, r = ∞. Setting x = -1,

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

error ≤~ 0.0002.

Adding up,

e^-1 ~ 0.36806, error ≤ 0.0002.

The actual value is e^-1 ~ 0.36788.