Tuesday, 21 May 2019

calculus - Find the sum of infinite series when ever the series converges.



Hi I am trying to find the sum of this infinite series whenever it converges. I have tried the common ratio technique but my work doesn't match the answers. I would appreciate any help with explanation.



k=1(2cos2θ)k


Answer




this is a geometric series. So answer is
2cos2θ12cos2θ


whenever
cos2θ<12


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