How do I determine if the following converges (using basic convergence tests: comparison, limit comparison, etc.) $\displaystyle \sum\sin\frac{1}{n}$
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Originally Posted by manyarrows How do I determine if the following converges (using basic convergence tests: comparison, limit comparison, etc.) $\displaystyle \sum\sin\frac{1}{n}$ Compare it to $\displaystyle \sum\frac{1}{n}$. Thus, it diverges. (See here for a similar problem.)
Even on [1,infinity] It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.
Originally Posted by manyarrows Even on [1,infinity] It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval. You should read this: http://en.wikipedia.org/wiki/Harmoni...s_(mathematics)
Originally Posted by manyarrows Even on [1,infinity] It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval. The series in question is not an alternating series.
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