\lim_{a\to 0} \left[
\left( 1^{n+1} \left( \frac{\ln 1}{n+1} - \frac{1}{(n+1)^2} \right) \right)- 
\left( a^{n+1} \left( \frac{\ln a}{n+1} - \frac{1}{(n+1)^2} \right) \right)
\right] =