Determine Whether the Sequence $a _ { \mathrm { n } } = \frac { n ^ { 4 } - 1 } { 5 - n ^ { 4 } }$

question 1

Essay

Determine whether the sequence $a _ { \mathrm { n } } = \frac { n ^ { 4 } - 1 } { 5 - n ^ { 4 } }$ converges or diverges. If it converges, find the limit.

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Definitions:

Unique Risk

Nonmarket or firm-specific risk factors that can be eliminated by diversification. Also called firm-specific risk, nonsystematic risk, or diversifiable risk.

Diversification

Diversification is an investment strategy that aims to reduce risk by allocating investments among various financial instruments, industries, geographic locations, or other categories.

Portfolio

A collection of investments, such as stocks, bonds, commodities, and real estate, held by an individual or an institution.

Index Model

A statistical model to estimate the returns of a stock based on the returns of a broader market index.