Answer by user230734 for Find a sequence $a_n$ such that its sum converges,...
In this case, it is easy to find a simple criterion. For $\sum \log(a_n)$ to converge, we should first have as a necessary condition $\log(a_n)$ converges to $0$ (by the limit test), and this only...
View ArticleFind a sequence $a_n$ such that its sum converges, but the sum of its...
This question came up in a past paper that I was doing, but it seems to be a fairly common, standard question. Give an example of a sequence $a_n$ such that $\sum(a_n)$ converges, but $\sum(\log(a_n))$...
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