Determine If the Series Converges or Diverges $$\sum _ { n = 1 } ^ { \infty } \left( \tan ^ { - 1 } ( n + 1 ) - \tan ^ { - 1 } n \right)$$

question 31

Multiple Choice

Determine if the series converges or diverges. If the series converges, find its sum.
- $$\sum _ { n = 1 } ^ { \infty } \left( \tan ^ { - 1 } ( n + 1 ) - \tan ^ { - 1 } n \right)$$

• A) converges; \(\frac { \pi } { 2 }\)
• B) converges; \(\pi\)
• C) diverges
• D) converges; \(- \frac { \pi } { 2 }\)

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Definitions:

Floatation Costs

Expenses incurred by a company in issuing new securities, including fees to underwriters, legal fees, and registration fees.

Firm Commitment

An agreement where an underwriter guarantees to buy and sell all securities from the issuing company at an agreed-upon price.

Underwriter

A financial specialist or institution that assesses and undertakes the risk of another entity, often seen in insurance and securities issuances.

Direct Costs

Expenses that can be directly attributed to the production of goods or services, such as materials and labor.