Hi, I'm trying to work out (limit as n=>infinity) (n * (sqrt(1 + 1/n) - 1)).
I know that by letting n = 1/t and then using l'hopitals this equals 1/2.
However, I need to use only basic limit rules (add/sub/mult/div and composition).
I feel like I am really close to the answer because I have been able to rewrite this as (n * (1 + 1/n)^(1/2)) - n.
I noted that:
ln(n * (1 + 1/n)^(1/2))) - ln(n)
= ln((1 + 1/n)^(1/2))
and since lim(1+1/n) = e as n=>inf
I cannot figure out any way to actually bring the ln into the equation like that though...any thoughts? Suggestions would be much appreciated.