Growth of Partial Sums of Divergent Series
Growth of Partial Sums of Divergent Series
Let $\Sigma f(n)$ be a divergent series of decreasing positive terms, with partial sums ${s_n}$, where f decreases sufficiently smoothly; let $\varphi (x) = \smallint _1^xf(t)dt$ and let $\psi$ be the inverse of $\varphi$. Let ${n_A}$ be the smallest integer n such that ${s_n} \geqslant A$ but ${s_{n - 1}} …