Let . We have , so and . The terms of this series have alternating signs and decreasing absolute values (when ); therefore, the sum from the th term to infinity is bounded by the th term. For example, let . Then .
Now, suppose . Then . Our goal is to make . One can check that , but , so we have to approximate f(x) with a partial sum of three terms, i.e., with g(x).
Calculating gives −0.019801778, which is −0.019802 when rounded to the 6th digit.