Polylogarithm series remainder bound ($|R_N|\le |z{|}^{N+1}/[(N+1{)}^a(1-|z|)]$)

For $|z|<1$, $a\ge 0$ and integer $N\ge 0$, truncating the defining polylogarithm power series after $N$ terms has remainderThe inequality uses monotonicity of $k^a$ and then the geometric series. The bound applies to negative real $z$ as well as positive real $z$, and gives a rigorous absolute truncation tolerance independently of cancellation. It does not bound floating-point rounding error.