Tell Which of the Following Three Series Cannot Be Found $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 2 + 3 ^ { n } }$

question 179

Multiple Choice

Tell which of the following three series cannot be found convergent by the Ratio Test but can be found convergent by comparison with a p-series.
1) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 2 + 3 ^ { n } }$
2) $\sum _ { n = 1 } ^ { \infty } \frac { n } { n ^ { 3 } + 4 }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { \sqrt { n } } { n ^ { 2 } + n }$

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

---

Definitions:

Intrinsic Value

The actual, inherent value of a financial security, determined through fundamental analysis without reference to its market value.

Put Option

A financial contract that gives the buyer the right, but not the obligation, to sell an asset at a specified price within a specific time frame.

Actual Value

Actual value refers to the true, inherent, or market value of an asset, not influenced by external conditions such as market fluctuations or investor perceptions.

Time Value

A concept stating the value of money is affected by time, primarily due to the potential earning capacity of money over time.