nsum convergence criteria about mpmath-2 HOT 2 OPEN

Hi Jan, thanks for the bug report.

I'm not sure if the proposed fix is sufficient, and it would slow down 
convergence of the direct method for well-behaved series.

I think there is a fairly easy workaround: explicitly add several terms at a 
time, say three: instead of

nsum(f, [1,inf])

do

nsum(lambda n: f(3*n-2) + f(3*n-1) + f(3*n), [1,inf])

Hi Fredrik,

Thank you for the workaround. However, there is still problem, that 
tolerance has different meaning in direct method and in extrapolation 
method. In the first case you measure only magnitude of terms in the 
second case you measure difference between individual steps.

If you woldn't touch convergence speed of direct method what about 
average over updated terms, this has straightforward counterpart in
extrapolation methods. The average has advantage that the meaning of 
tolerance is "independent" of the value of steps.

Jan