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Determine Whether the Sequence Defined By an=n256n2+1a _ { n } = \frac { n ^ { 2 } - 5 } { 6 n ^ { 2 } + 1 }

question 15

Multiple Choice

Determine whether the sequence defined by an=n256n2+1a _ { n } = \frac { n ^ { 2 } - 5 } { 6 n ^ { 2 } + 1 } converges or diverges. If it converges, find its limit.


Definitions:

Sample

A Sample refers to a subset of a population used in statistical analysis, mathematically selected to estimate characteristics of the whole population.

Polyamides

A type of polymer made up of repeating units linked by amide bonds, commonly found in materials like nylon.

Crystalline Polymers

Polymers characterized by a regular, ordered arrangement of molecules in a lattice structure, leading to distinct melting points and high degrees of strength and transparency.

Nonvolatile Liquids

Liquids that have low vapor pressures at room temperature and do not readily evaporate into the atmosphere.

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