Truncation error

Example:

> exp(Pi/4);evalf(%);

> ser1:=sum(x^(i)/((i)!),i=0..2);

> appr:=evalf(subs(x=Pi/4,ser1));

> truncation:=evalf(exp(Pi/4)-appr);

The above graph illustrates how the truncation error decreases when more terms are retained in the series.

The Truncation Error is caused by the shortcomings of the method of approximation, and will be present even if one could calculate with infinite accuracy!

Because the Truncation Error depends on the method of approximation, it can often be estimated.