The factorial can only be computed manually, no ready function to use.
If by this you mean there is no function in the STL I believe you are correct, but if you mean you can't have a function that find a factorial you are not correct. You can find a factorial pretty easy by using recursion. I believe there might also be one in the boost library also but I'm not sure.
Often when calculating the sum of a series, it isn't necessary to calculate the complete factorial each time. Usually, there is a simple relationship between successive terms of the series. Just one or two multiplications or divisions are sufficient to derive each term from the previous one.