Plotting the series $\displaystyle y = \sum_{k} \frac{\sin kx }{k}$
In the limit it would look like
Taking a finite number of terms, I want to understand what is the reason for the jiggling at the extremes, while there the jiggling in the middle is so small its not noticable.
I truncated the sum to $1,2,3\; \mbox{and}\;4$ terms but cannot deduce much of a reason.
The "jiggling" was noticeable here because the sum is linear in the limit, however, for an expression like $p(x) = x\prod_k\Big(1-\frac{x^2}{k^2\pi^2}\Big) $
Does the truncated expression oscillate back and forth the limit?