Do the Following Sequences Converge or Diverge? If They Converge $\left\{\frac{5 n}{2 n+1}\right\}$

question 27

Essay

Do the following sequences converge or diverge? If they converge, state the limit.
(a) $\left\{\frac{5 n}{2 n+1}\right\}$
(b) $\left\{\frac{n^{3}+1}{2 n+1}\right\}$
(c) $\left\{\frac{3 n^{3}}{4 n^{5}+1}\right\}$

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Definitions:

Inventory

The quantity of goods or materials on hand at a particular time, held by a business to support production or meet customer demand.

Predictable Variability

Predictable variability refers to fluctuations in data, processes, or systems that, although variable, can be forecasted or anticipated based on historical patterns.

Trade Promotions

Marketing activities executed to increase product demand, typically through discounts or special offers to retailers or wholesalers.

Subcontracting

The practice of hiring a third party to perform tasks, provide services, or conduct operations that are normally or could be done in-house.