Question

I need help with a limit:

lim t->infinity [ln(t+1/t+2)-ln(1/2)]
My solution manual says you should end up with ln(1)-ln(2)=ln(2), however I dont know how they got to the ln(2).

Answer 1

\[\lim_{t \rightarrow \infty} [\ln ((t+1)/(t+2))-\ln (1/2)]\]

Answer 2

\[\frac{t+1}{t+2}\to 1\text{ as }t\to\infty\]
\[\ln(1)=0\]
\[-\ln(1/2)=\ln(2)\]

Answer 3

\[-\ln\left(\frac{1}{2}\right)=\ln\left(\left(\frac{1}{2}\right)^{-1}\right)=\ln(2)\]

Answer 4

Okay I get it now, that you Zarkon!