Chapter 6.7, Problem 56E

To determine

To find: The recursive formula for the pattern of Pascal’s triangle.

Answer to Problem 56E

The recursive rule will be:

  $\begin{array}{l}{1}_1=1,\\ m_n={\left(m-1\right)}_{n-1}+m_{n-1}\end{array}$

Explanation of Solution

Given information:

The given m^thnumber in the n^th row as shown below,

  

Formula used:

The m^th number or term in any row (starting from second row) is the sum of the ( m − 1 )th & m^th number of the previous row.

Calculation:

Starting at the 2^nd row (1, 1), the m^th number or term is the sum of the (m − 1)th & m^th number of the previous row.

Let $m_n$ be the m^th term in nth row.

Example: $6=3_5$ (third term in 5^th row)

The recursive rule will be:

  $\begin{array}{l}{1}_1=1,\\ m_n={\left(m-1\right)}_{n-1}+m_{n-1}\end{array}$

The recursive rule will be:

  $\begin{array}{l}{1}_1=1,\\ m_n={\left(m-1\right)}_{n-1}+m_{n-1}\end{array}$