Final answer:
The series Σ(-1)^n * π^(2n+1) / (6^(2n+1) * (2n)!) does not correspond to a known series expansion, and without additional information like the range of n or a related function, the sum cannot be determined.
Step-by-step explanation:
To find the sum of the series given by Σ(-1)^n * π^(2n+1) / (6^(2n+1) * (2n)!), one would typically see if the series corresponds to a known series expansion. However, this series does not directly match standard series expansions such as the Binomial theorem or other elementary functions. As such, without further context like a range for n or the relation of this series to a known function, we cannot provide a sum for the series. It's possible that this series could be a part of a more complex function or require a deeper understanding of convergence or divergence of series. Typically, the resolution of such a complex series would be tackled in a college-level mathematics course.