Find the Sum of the Series $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } \pi ^ { 2 n + 1 } } { 3 ^ { 2 n } ( 2 n + 1 ) ! }$

question 69

Short Answer

Find the sum of the series $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } \pi ^ { 2 n + 1 } } { 3 ^ { 2 n } ( 2 n + 1 ) ! }$ .

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Definitions:

Initial Endowment

The initial quantity of goods, services, or resources an individual, firm, or economy possesses.

Pareto Efficient

A state of allocation where it is impossible to make any one individual better off without making at least one individual worse off.

Utility Function

A mathematical representation that ranks the preferences of an individual consumer for different bundles of goods.

Initial Endowment

The original allocation of resources, including assets and goods, available to an individual or entity at the start of an economic analysis.