how to find that summation by Mathematica Wolfram $\displaystyle \sum_{x\in A} \sin(\pi x) $ $\displaystyle A={{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},........ .}}$
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Originally Posted by nice rose how to find that summation by Mathematica Wolfram $\displaystyle \sum_{x\in A} \sin(\pi x) $ $\displaystyle A={{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},........ .}}$ Input: Sum[Sin[Pi/n], {n, 1, Infinity}]. Message: Sum::div: Sum does not converge.
Originally Posted by nice rose how to find that summation by Mathematica Wolfram $\displaystyle \sum_{x\in A} \sin(\pi x) $ $\displaystyle A={{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},........ .}}$ Since for small $\displaystyle u$ we have $\displaystyle \sin(u)\approx u$ this is obviously not convergent as the tail of the sum behaves like the harmonic series which is known to be divergent. . CB
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