is the following alternating series divergent or convergent series? (please show proof) ∞ ∑ (-1)^(n-1) cos(1/n) n=1

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is the following alternating series divergent or convergent series? (please show proof) ∞ ∑ (-1)^(n-1) cos(1/n) n=1

Mathematics
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Set your series = a(n). Then use a(n+1) like this: |a(n+1)/a(n)| Working this you will find eventually find: cos(1/n+1)/cos(1/n) which should evaluate to <1 and therefore be absolute convergent. I'm not used to evaluating series with trigonometric components though.
doesnt that go to 1 and not < 1 since we take the limit to infinity using the ratio test
You might be correct in that, I'm not a 100% sure, been a while since I did the infinite series. If it does evaluate to 1, you'd need to consider the different cases and evaluate from there.

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