Which One of the Following Series Is Divergent?
A) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 } { 3 } \right) ^ { n }$

question 134

Multiple Choice

Which one of the following series is divergent?

• A) \(\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 } { 3 } \right) ^ { n }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 2 } + 1 }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n 5 ^ { n } }\)
• D) \(\sum _ { n = 2 } ^ { \infty } \frac { n } { n ^ { 2 } - 1 }\)
• E) \(\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 3 } } { n ^ { 5 } + 2 }\)
• F) \(\sum _ { n = 1 } ^ { \infty } \frac { 2 ^ { n } } { n ! }\)
• G) \(\sum _ { n = 1 } ^ { \infty } \frac { \pi } { n ^ { 2 } }\)
• H) \(\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { \pi } { n }\)

Calculate the price of bonds with different maturities, coupon rates, and yield to maturities.

Identify different shapes of yield curves (normal, inverse, flat) and understand their economic implications.

Apply the term structure of interest rates to estimate future interest rates and bond valuations.

Analyze forward rates and their relationship to yield to maturity and interest rates.

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Definitions:

Algorithmic

Pertaining to or using a set of rules to be followed in calculations or other problem-solving operations, especially by a computer.

Heuristic

A shortcut (rule of thumb or informal guideline) used to reduce the amount of thinking that is needed to make decisions.

Informal Reasoning

The process of thinking about issues in a non-formal or structured manner, often used in everyday problem-solving and decision-making.

Schemas

Cognitive frameworks or concepts that help individuals organize and interpret information from the world around them, influencing learning and perception.