Hi Thomas,
thanks for your interest. Whenever there is something not in our
documentation, but you suspect sympy can do, try to look into tests
(all functionality is tested for, or at least should be). In this
particular case, look into:
http://hg.sympy.org/sympy/file/9b08e6f28e3e/sympy/concrete/tests/test_sums_products.py
You'll find there plenty of examples, e.g.:
In [1]: var("n")
Out[1]: n
In [2]: sum(2**(-n), (n, 1, oo))
Out[2]: 1
In [3]: sum(2**(-4*n+3), (n, 1, oo))
Out[3]: 8/15
If you discover some sums, that are not working, you can try to look
how it is implemented and maybe try to figure out how to fix it. We'll
help you prepare any patches.
As to your question about mpmath, you can access mpmath easily from sympy:
from sympy.thirdparty import mpmath
Let us ask, if you have more quesitons.
Ondrej