Determine Whether the Given Series Is Convergent (But Not Absolutely $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } n } { n ^ { 2 } + 1 }$

question 266

Short Answer

Determine whether the given series is convergent (but not absolutely convergent), absolutely convergent, or divergent. $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } n } { n ^ { 2 } + 1 }$

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Definitions:

Predetermined Overhead Rate

A predetermined rate employed to allocate estimated manufacturing overhead costs to products, calculated before the period starts, using projected costs and activity levels.

Direct Labour Hour

A measure of labor that directly contributes to the production of goods, used in calculating labor costs and efficiency.

Manufacturing Overhead

All manufacturing costs that are not directly associated with the production of a product, including costs related to indirect materials, indirect labor, and other indirect expenses.

Overapplied Overhead

This occurs when the overhead allocated to products or job orders during a period exceeds the actual overhead costs incurred.