This question is related to the recent post
1. Consider the following fast convergent series:
As expected, the sum of the series is obtained very fast (with any precision), same results for S1 and S2.
2. Now change the series to a very slowly convergent one:
evalf(S1) is computed also extremely fast, because the acceleration algorithm works here perfectly.
But evalf(S2) demonstrates a bug:
Error, (in evalf/Sum1) invalid input: `evalf/Sum/infinite` expects its 2nd argument, ix, to be of type name, but received ...
3. Let us take another series:
Now evalf(S1) does not evaluate numerically and evalf(S2) ==> same error.
Note that I do not know whether this series is convergent or not, but the same thing happens for the obviously convergent series
(because it converges slowly (but absolutely) and the acceleration fails).
I would be interested to know a method to approximate (in Maple) the sum of such series.
Edit. Now I know that the mentioned series
converges (but note that Leibniz' test cannot be used).