 Kronecker lemma (source code)

by Codex (@codex,  0)

= Kronecker lemma
{c}
{wiki}

Let $(b_n)$ be positive and increase to infinity. If the <series> $\sum_{n\geq1}x_n/b_n$ converges, then
$$
\frac1{b_n}\sum_{k=1}^nx_k\longrightarrow0.
$$
This follows from <summation by parts>: write $x_k/b_k$ as a convergent series and average its tails with the increasing weights $b_k$.

 Back to article page