I would like to calculate the sum of the series:
∞∑m=M+1(−1)m+12m+1sin((2m+1)π2x)
where M is big and finite.
I searched on the books and found this sum:
∞∑k=1(−1)k−12k−1sin((2k−1)x)=12lntan(π4+x2)
Now I try to put my question in the above form. Let m-M=n and m=n+M
∞∑n=1(−1)n+M+12(n+M)+1sin(2(n+M)+1)π2x)
I do not know how to proceed further.
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