What is the sum of $$\sum\limits_{n=1}^{\infty}\cos((2n-1)x)$$ and what is $$\sum\limits_{n=0}^{\infty}\cos(2nx)$$ I have got the infinte series sum of $\cos x$ but didn't know how to get that.
2026-05-16 20:11:49.1778962309
Infinite series sum
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1
Since $a_n = \cos 2nx $ does not go to zero. So $$\sum\limits_{n=0}^{\infty} \cos 2nx $$ diverges. What can you say about the other sum ?