Which of the Following Series Are Convergent, but Not Absolutely $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \frac { n + 2 } { n ^ { 2 } + 1 }$

question 20

Multiple Choice

Which of the following series are convergent, but not absolutely convergent?
1) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \frac { n + 2 } { n ^ { 2 } + 1 }$
2) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { n ^ { 4 } }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } n } { n + 1 }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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Definitions:

New Equity Sales

The process of selling new shares of a company to investors to raise capital.

Residual Policy

A financial strategy where dividends are paid to shareholders from the remaining or residual net income after all operating and expansion expenses.

Compromise Policy

A compromise policy is a policy that is agreed upon through concessions from all parties involved, aiming for a middle ground solution.

Debt/Equity Ratio

Debt/Equity Ratio is a financial ratio indicating the relative proportion of shareholders' equity and debt used to finance a company's assets.