%\noindent\textbf{\large Binomial Coefficients}
\section{Binomial Coefficients}

{\small
\begin{align}
\nonumber
  (x+y)^n &= x^n + {n\choose 1}x^{n-1}y + {n\choose 2} x^{x-2}y^2
            + \cdots + {n\choose n}y^n \\
\nonumber
       & = \sum_{k=0}^{n} {n\choose k}x^{n - k}y^k
\end{align}
}

\begin{displaymath}
  {n\choose k} + {n \choose k + 1} = {n + 1 \choose k + 1}
\end{displaymath}

\begin{displaymath}
  \sum_{k=0}^n {n\choose k} = 2^n
\end{displaymath}

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