i belive it will never converge unless the intire function is zero (exept a finite number of values)

or

that the function is un-even in weak form ( f(c-x)=-f(c+x) for x in[a,b] or (a,b)* when c = (a+b) / 2 the sum is f(c) )

*if the interval is closed only in one side then add this side to the sum