Hello Everyone! Today we are asked to find an an approximation for f(x) that gives a finite sum values for all x where f(x) is defined as $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}\sin(nx)$. I don't know if I rephrased it right, but the exact problem goes like this:

"

*What does the statement* $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}\sin(nx)$

*mean? Can you write down a ﬁnite sum approximation of f(x)?*"

Since this one resembles a fourier sine series, my first guess is to find the exact function,f(x), such that $\displaystyle \frac{1}{n}=\frac{2}{\pi}\int_{0}^{\pi}f(x)sin(nx) dx$

But from there I'm lost as to how I would find f(x). Anyone got any idea to find f(x) or at least find an approximation of it? Thanks everyone in advance!