I'm continuing to have trouble similar to what I described above. Now, however, I'm trying to integrate the expression:
$\frac{\sum_{n=0}^N{\sin(nx)}}{\sum_{n=0}^N{(a_n + \cos(nx) + \sin(nx))}}\tag{1}$
My input into Wolfram Alpha is: sum(sin(n*x)) from n = 0 to 1 / (sum(a_n + cos(n*x) + sin(n*x))) from n = 0 to 1. This gives exactly Equation 1 with N = 1, as expected, and changing N changes the sum.
However, I can't get it to actually integrate this expression. Adding the word integrate in front somehow causes it to interpret the whole thing as (sin(n*x))! Adding the word antiderivative to the end instead causes it to try to integrate the denominator alone (and causes computation time to be exceeded, but that's a separate issue). Finally, putting the original expression in parentheses and adding the word integral to the end causes it to interpret the input as... sin.
I really don't understand what I'm doing wrong. Please help.
