Series truncation error
= Series truncation error
{title2=$R_N=S-\sum_{n=1}^{N}a_n$}
For a <convergent series> with <sum> $S$, the error from keeping only the first $N$ terms is the remaining <sum> $R_N=\sum_{n>N}a_n$. This <truncation error> exists even with exact arithmetic. The <zeta series truncation error> gives explicit bounds for positive reciprocal-power terms.