Test the Following Series for Convergence or Divergence $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { n ^ { 2 } } { n ^ { 2 } + 1 }$

question 141

Short Answer

Test the following series for convergence or divergence: $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { n ^ { 2 } } { n ^ { 2 } + 1 }$ .

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Definitions:

Terms 2/10 n/30

Payment terms indicating a 2% discount if paid within 10 days, otherwise the full amount is due within 30 days.

Physical Inventory Count

An assessment method where a business physically counts its entire inventory to verify stock records and accounts.

Perpetual Inventory System

An inventory management method where updates to inventory records are made in real-time following each receipt or sale of inventory items.

Periodic Inventory System

An inventory accounting system where the inventory is updated in the accounting records periodically, typically at the end of an accounting period, rather than after each transaction.