What is Truncation error?

In numerical analysis and scientific computing, truncation error is an error caused by approximating a mathematical process.

Example 1:

A summation series for e x {\displaystyle e^{x}} is given by an infinite series such as

e x = 1 + x + x 2 2 ! + x 3 3 ! + x 4 4 ! + . . . . . {\displaystyle e^{x}=1+x+{\frac {x^{2}}{2!}}+{\frac {x^{3}}{3!}}+{\frac {x^{4}}{4!}}+.....}