Find the Sum of the Series $\frac { 2 } { 1.3 } - \frac { 2 ^ { 2 } } { 2.3 ^ { 2 } } + \frac { 2 ^ { 3 } } { 3.3 ^ { 3 } } - \frac { 2 ^ { 4 } } { 4.3 ^ { 4 } } + \ldots$

question 136

Multiple Choice

Find the sum of the series. $\frac { 2 } { 1.3 } - \frac { 2 ^ { 2 } } { 2.3 ^ { 2 } } + \frac { 2 ^ { 3 } } { 3.3 ^ { 3 } } - \frac { 2 ^ { 4 } } { 4.3 ^ { 4 } } + \ldots$

• A) \(\ln \left( \frac { 1 } { 3 } \right)\)
• B) \(\ln \left( \frac { 4 } { 3 } \right)\)
• C) \(\ln \left( \frac { 5 } { 3 } \right)\)
• D) \(\frac { 5 e } { 3 }\)
• E) \(e ^ { 5 / 3 }\)

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Definitions:

Acid-test Ratio

A financial metric that assesses a company's ability to pay off its short-term liabilities with its most liquid assets, excluding inventory.

Return on Assets

A financial ratio that indicates how efficiently a company uses its assets to generate profit, calculated as net income divided by total assets.

Debt/assets Ratio

A financial ratio that compares the total amount of debt a company has to its total assets, indicating how much of the assets are financed by debt.

Current Ratio

Current Ratio is a liquidity ratio that measures a company's ability to pay short-term obligations or those due within one year.