(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

To find the limit of the sequence (I suppose it is zero)

[tex] \lim \frac{\sqrt{n+1}}{n}[/tex]

2. Relevant equations

The limit is zero if for every [itex] \epsilon > 0[/itex] there exists [itex]n_0[/itex] such that for all [itex]n \geq n_0[/itex] one has

[tex]|a_n - 0| < \epsilon [/tex]

or what is the same

[tex]-\epsilon < a_n < +\epsilon[/tex]

3. The attempt at a solution

Tried writing it as

[tex](n+1)^{1/2} n^{-1}[/tex]

but have no idea what to do next.

I know I can think the associated differentiable function [tex]f(x) = \frac{\sqrt{x+1}}{x}[/tex] and use L'Hopital, but that would be cheating, as this concept is previous to the limit of functions.

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# Homework Help: \lim_{n \to \infty} \sqrt(n+1)/n

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