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Math Help - Pascal's Triangle.

  1. #1
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    Pascal's Triangle.

    How do i solve these... i get the pattern is pascals triangle but how do i use the pascal identity in the equation (please do a or b.. im not assigned to do them) ;/
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  2. #2
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    The pascal identity states for all positive integers we have,
    \left(\begin{array}{c}n\\m-1\end{array}\right) +\left(\begin{array}{c}n\\m\end{array}\right)=<br />
\left(\begin{array}{c}n+1\\m\end{array}\right)

    Thus, we have,
    ---------
    \left(\begin{array}{c}10\\2\end{array}\right)+<br />
\left(\begin{array}{c}10\\3\end{array}\right)=<br />
\left(\begin{array}{c}11\\3\end{array}\right)

    \left(\begin{array}{c}15\\14\end{array}\right)+<br />
\left(\begin{array}{c}15\\15\end{array}\right)=<br />
\left(\begin{array}{c}16\\15\end{array}\right)

    \left(\begin{array}{c}20\\18\end{array}\right)+<br />
\left(\begin{array}{c}20\\19\end{array}\right)=<br />
\left(\begin{array}{c}21\\19\end{array}\right)

    \left(\begin{array}{c}n\\r-2\end{array}\right)+<br />
\left(\begin{array}{c}n\\r-1\end{array}\right)=<br />
\left(\begin{array}{c}n+1\\r-1\end{array}\right)
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