(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**