Question

find the limit of the sequence, using lhôpitals rule when appropriate.

\\\frac{\sqrt{n}}{\sqrt{n} + 1}\\

Explanation:

Express the limit of the sequence

$$ L = \lim_{n \to \infty} \frac{\sqrt{n}}{\sqrt{n} + 1} $$

Divide numerator and denominator by \(\sqrt{n}\)

$$ L = \lim_{n \to \infty} \frac{1}{1 + \frac{1}{\sqrt{n}}} $$

Evaluate the limit

$$ L = \frac{1}{1 + 0} = 1 $$

Answer:

Find the limit of the sequence, using L'Hôpital's rule when appropriate.

$$\frac{\sqrt{n}}{\sqrt{n} + 1}$$

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