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In Course Notes 10, we have shown that $H_n\sim\ln n$. 
Therefore, 
\[
  \sum_{i=1}^n 6/i =6H_n \sim 6\ln n \sim 6\ln n + 2= 2\ln (n^3)+2 \ldotp
\]

We can prove $6\ln n \sim 6\ln n +2$ by
\begin{align*}
\lim_{n\rightarrow \infty} \frac{6\ln n+2}{6\ln n}
=\lim_{n\rightarrow \infty} \left( 1 + \frac{2}{6\ln n}\right)=1
\end{align*}

Common mistakes of this problem include claiming
\[
\frac{\infty}{\infty}=1
\]
and not citing or proving $H_n\sim \ln n$.


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