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\title{Class work: Summations}

\date{}
\maketitle

Find a tight bound for the following summations: 


\begin{enumerate}

\item $1 + 2 + 3 + .... + \lg n$
\vspace{1cm}

\item $1+ 2 + 3 + 4+ .... +  n^2$
\vspace{1cm}

\item $1 + 1/2 + 1/2^2 + ... + 1/2^n$
\vspace{1cm}

\item $1 + 1/5 + 1/5^2 + ... + 1/5^n$
\vspace{1cm}

\item $\frac{9}{10} + {(\frac{9}{10})}^2 + ... + {(\frac{9}{10})}^n$
\vspace{1cm}

\item $\frac{2}{3} + {(\frac{2}{3})}^2 + ... + {(\frac{2}{3})}^{\lg n}$
\vspace{1cm}

\item $1 + 2  + 2^2 + 2^3 + ... 2^n$
\vspace{1cm}

\item $1+ 2  + 2^2 + 2^3 + ... 2^{n^2}$
\vspace{1cm}

\item $n + \frac{n}{2} +  \frac{n}{4} + ... $
\vspace{1cm}


\item $n + \frac{2n}{3} +  \frac{4n}{9} +  ... $
\vspace{1cm}

\item $n + \frac{99n}{100} +  \frac{99^2n}{100^2} +  ... $
\vspace{1cm}

\end{enumerate}

\end{document}
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