I'm trying to find out whether the series $$\sum\limits_{n=1}^{\infty}(-1)^n\ln\left[\frac{8n+2}{7n+1}\right]$$ converges or not, but the alternating series test seems not to apply. What other tests can I use? Does this series converges or diverges?
2026-04-02 10:33:02.1775125982
Does the alternating series converge: $\sum\limits_{n=1}^{\infty}(-1)^n\ln\left[\frac{8n+2}{7n+1}\right]$?
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$$\log\frac{8n+2}{7n+1}\xrightarrow[n\to\infty]{}\log\frac87\neq0$$
and thus
$$(-1)^n\log\frac{8n+2}{7n+1}\rlap{\;\;\;\;/}\xrightarrow[n\to\infty]{}0\implies\text{ the series cannot converge}$$