Fuente TeX:

\displaystyle \log\left( \frac{n^2+2n+1}{n^2} \right) = \log\left( \frac{(n+1)^2}{n^2} \right) = 2 \log \left( \frac{n+1}{n} \right) = 2 \log \left( 1+\frac{1}{n} \right)