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

question 156

Short Answer

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

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Definitions:

Increasing Returns to Scale

A situation in which a proportional increase in all inputs results in a more than proportional increase in output, demonstrating economies of scale.

Law of Diminishing Returns

An economic principle stating that, holding all else constant, as one input variable is increased, there is a point at which the marginal per unit output starts decreasing.

Diseconomies of Scale

The phenomenon where an increase in production leads to higher per-unit costs, often due to inefficiencies associated with scale.