Find the Exact Value of the Limit of the Sequence $a _ { 1 } = \sqrt { 4 } , a _ { n + 1 } = \sqrt { 4 + a _ { n } }$

question 39

Short Answer

Find the exact value of the limit of the sequence defined by $a _ { 1 } = \sqrt { 4 } , a _ { n + 1 } = \sqrt { 4 + a _ { n } }$ .

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Definitions:

Near Point

The closest distance at which an object can be seen clearly by the eye, a measure of the eye's accommodation ability.

Accommodation

The process by which the eye changes optical power to maintain a clear image or focus on an object as its distance varies.

Elastic

Capable of returning to its original shape after being stretched or compressed, a property of certain materials.

Sclera

The white, outer layer of the eyeball that provides protection and shape.