Find the limit of a sequence involving a polynomial divided by the square root of a polynomial as n approaches infinity.

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Limit of a Sequence with a Square Root

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\( a_{n}=\frac{n^{2}+5}{\sqrt{4n^{4}+n}} \)

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What you need first

algebraic manipulation of fractions and square roots
evaluating limits of the form c/n^p as n approaches infinity
limit laws for sequences

What this problem tests

Tests the ability to identify the dominant term in an algebraic expression and correctly manipulate expressions inside and outside of a square root to evaluate a limit at infinity.

This is a standard introductory problem in Calculus II or Real Analysis when learning how to evaluate limits of sequences.

Limit of a Sequence with a Square Root

What you need first

What this problem tests

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