How Many Terms of the Alternating Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ^ { - 2 }$

question 116

Multiple Choice

How many terms of the alternating series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ^ { - 2 }$ must we add in order to be sure that the partial sum $S _ { n }$ is within 0.0001 of the sum $S$ ?

• A)10
• B)300
• C)30,000
• D)30
• E)3
• F)10,000
• G)100
• H)1000

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Definitions:

Nash Equilibrium

A concept in game theory where no player can benefit by unilaterally changing their strategy if the strategies of the other players remain unchanged.

Simultaneous Game

A simultaneous game is a type of game in game theory where all players make their decisions or moves at the same time without knowledge of the others' choices.

Payoff Matrix

A strategic analysis tool used in decision theory and game theory that shows the potential outcomes and payoffs from different decisions made by two or more players.

First-Mover Advantage

The competitive edge that a company gains by being the first to market with a product or service.