CAS programs, order of LOCAL variables?

[Helge Gabert]

Also, the CAS knows the limit of the infinite sum of the above series

sum(j=1, infinity, ((-1)^(j+1))/(2*j-1)) - - pi/4

but it doesn't seem to know the limit of the related, alternating harmonic series

sum(j=1, infinity, ((-1)^(j+1))/j) - - ln(2)

I wonder if the CAS employs a lookup table, or if it tries out various convergence criteria.