Determine Whether the Sequence $a _ { n } = \lim _ { n \rightarrow \infty } \frac { 5 } { 4 n ^ { 4 } } \left[ \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } \right]$

question 33

Essay

Determine whether the sequence $a _ { n } = \lim _ { n \rightarrow \infty } \frac { 5 } { 4 n ^ { 4 } } \left[ \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } \right]$ converges or diverges. If it converges, find the limit.

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Definitions:

Prestige Pricing

Psychological pricing strategy used with goods whose quality is difficult to determine by inspection or for products about which consumers have little solid information.

Price Skimming

Setting the price of a new product higher than expected to recover development costs.

Penetration Pricing

Setting the price of a new product lower than expected to gain fast market share.

Development Costs

Development costs are expenses associated with the creation and design of new products or services, including research and development.