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{\bfseries CSE\,105: Automata and Computability Theory \hfill Fall 2015}
\begin{center}\huge Homework \#1 Solutions\end{center}
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\noindent\textbf{Solution to Problem 2}

\begin{theorem}
  For any positive integer $n$,
  \[ \sum_{k=1}^n k\cdot 2^{k-1} = 1 + (n-1) \cdot 2^n. \]
\end{theorem}
\begin{proof}

% PROBLEM 2 SOLUTION GOES HERE

\end{proof}


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