People here do not hate symsum(), but many people try to use symsum() for things it was not intended for.
syms x i n
y = symsum((-1)^i * x^(2*i+1)/factorial(2*i+1), i, 0, n)
See, it worked fine. It just doesn't tell you anything useful because MATLAB does not happen to recognize the pattern as matching any special function.
y20 = subs(y, n, 20)
fplot(y20, [-3 3])
subs(y, n, inf)
... it did not recognize the pattern because it was truncated. You can see that if you let n approach infinity then symsum() recognizes the pattern.
A lot of people try to use symsum() to do indexing, like symsum(x(i)^2/factorial(i), i, 1, 10) but you can never index with a symbolic variable so symsum cannot do that.
symsum() should mostly be reserved for finding formulas, the way that with inf it was able to find the sin() formula. In cases where you are using it to add a bunch of terms, a finite number of them, then most often it is better to construct the sequence of terms and sum() them.
