Truncation error

In numerical analysis and scientific computing, truncation error is the error made by truncating an infinite sum and approximating it by a finite sum. For instance, if we approximate the sine function by the first two non-zero term of its Taylor series, as in $\sin(x) \approx x - \tfrac16 x^3$ for small $x$, the resulting error is a truncation error. It is present even with infinite-precision arithmetic, because it is caused by truncation of the infinite Taylor series to form the algorithm.