Let \(\displaystyle S_n = \sum_{j=1}^n\sin(\sqrt{j\,}\pi)\). Show \(S_{(2M)^2}<0\) and \(S_{(2M+1)^2}>0\quad (M=1,2,3,...)\) .

2022-02-08

Let Sn=j=1nsin(jπ).

Show S(2M)2<0 and S(2M+1)2>0(M=1,2,3,...) .

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