# help me in Mathematica

#### nice rose

how to find that summation by Mathematica Wolfram

$$\displaystyle \sum_{x\in A} \sin(\pi x)$$

$$\displaystyle A={{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},.........}}$$

#### undefined

MHF Hall of Honor
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.

#### CaptainBlack

MHF Hall of Fame
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