Chapter 9, Problem 75RE

Solution

To state: The 9^th row of Pascal’s triangle.

The 9^th row is $1,9,36,88,126,126,84,36,9,1$ .

Given information:

The given statement says to find the row 9 of Pascal’s triangle.

Explanation:

Pascal’s triangle has a 1 at the top, with 1’s on the left and right edges of the triangle. The other values in the Pascal’s triangle are obtained by adding the two values above the position which follows:

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

The row 9 of Pascal’s triangle can be found out as.

  

So, the element of the 9th row of the Pascal’s triangle is 1, 9, 36, 84, 126, 126, 84, 36, 9, 1.