# Pascal's Triangle.

• March 27th 2006, 10:16 AM
Arbitur
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) ;/
• March 27th 2006, 03:22 PM
ThePerfectHacker
The pascal identity states for all positive integers we have,
$\left(\begin{array}{c}n\\m-1\end{array}\right) +\left(\begin{array}{c}n\\m\end{array}\right)=
\left(\begin{array}{c}n+1\\m\end{array}\right)$

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

$\left(\begin{array}{c}15\\14\end{array}\right)+
\left(\begin{array}{c}15\\15\end{array}\right)=
\left(\begin{array}{c}16\\15\end{array}\right)$

$\left(\begin{array}{c}20\\18\end{array}\right)+
\left(\begin{array}{c}20\\19\end{array}\right)=
\left(\begin{array}{c}21\\19\end{array}\right)$

$\left(\begin{array}{c}n\\r-2\end{array}\right)+
\left(\begin{array}{c}n\\r-1\end{array}\right)=
\left(\begin{array}{c}n+1\\r-1\end{array}\right)$