\documentclass{article}
\usepackage{enumerate}
\usepackage{amsmath}
\usepackage{hyperref}
\pagenumbering{gobble}
\begin{document}
\noindent\underline{Honors HW6} (due 27 March) \\
\noindent The important Euler-Mascheroni constant $\gamma$ is defined by
\[ \gamma \stackrel{\text{def}}{=} \displaystyle\lim_{n \rightarrow \infty} \left( \dfrac{1}{1} + \dfrac{1}{2} + \dfrac{1}{3} + \ldots + \dfrac{1}{n} - \log(n) \right).\]
This number appears in \href{https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant#Appearances}{many} different places in mathematics and science. In this homework, you will approximate this number. Define the sequence
\[ T_n = \dfrac{1}{1} + \dfrac{1}{2} + \dfrac{1}{3} + \ldots + \dfrac{1}{n} - \log(n). \]

\hrule 
\begin{enumerate}[1.]
\item It turns out that the sequence $a_n=\dfrac{1}{n}$ creates a divergent infinite sum (the ``harmonic series"). Use a spreadsheet (or write a computer program) to find the first $n$ for which $S_n>5$. 
\item Find the first $n$ for which $S_n>7$.
\item Compute $T_n$ for $n=1,2,3,4,5$, and $6$.
\item Use a spreadsheet or a computer program to find $T_{1000}$.
\end{enumerate}

\end{document}