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% Semester, course, title
\def\semester{Spring 2014 }
\def\course{Math 2710 }
\def\title{Homework 7 (Due Tues, Mar 25)}

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\rhead{First and Last Name} % enter your name here


\begin{document}

% Header
\vspace*{.8in} 
	\noindent {\raggedright{\bf \Large \title}
	\vspace*{.2in}
	
	\hspace*{1in}{\bf \course -- \semester}
	
	\vspace*{.05in}
	
	\hspace*{1in}{\bf  Professor Hohn} 
}
\vspace*{.2in}

% Numbered problems for homework
\begin{enumerate}

\item Prove that the inequality $n^2\geq n$ holds {\it for every integer}.
	
% Insert proof below
		\begin{proof}
			
		\end{proof}

\item (pg.105 \#33) Use induction to prove that 
\[
	\frac{1}{1} + \frac{1}{2} + \frac{1}{3}+\ldots + \frac{1}{2^n}\geq 1+ \frac{n}{2}\,.
\]
		
% Insert proof below
		\begin{proof}
			
		\end{proof}
		
		


\item (pg. 108 \#63) If $\displaystyle a=\frac{1+\sqrt{5}}{2}$ and $\displaystyle b=\frac{1-\sqrt{5}}{2}$, prove that $\displaystyle f_n=\frac{a^n-b^n}{\sqrt{5}}$ for all $n\in\N$.

% Insert proof below
		\begin{proof}
			
		\end{proof}


\end{enumerate}

\end{document}