Sunday, 3 August 2014

calculus - Test for convergence/divergence of suminftyn=1(1)nsinleft(fracnpiright)



Given the series





n=1(1)nsin(nπ)




I need to test for convergence/divergence. I think the divergent test might work here. I could see that the limn(1)nsin(nπ) might not exist, so the series is divergent. But I still need a solid proof here.



Any help is appreciated. Thanks.


Answer



I guess the standard argument should work. If Sn=nk=0ak converges then ak0. The necessary condition is not satisfied.


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