Chapter 11.7, Problem 23WE

a.

To determine

To find the sum of entries in each of the first $7$ rows of Pascal’s triangle.

Answer to Problem 23WE

  $1+2+4+8+16+32+64=127$

Explanation of Solution

The following is the Pascal’s triangle-

  

The Pascal’s triangle for 7 rows and can be added as follows-

  $1+2+4+8+16+32+64=127$

b.

To determine

To find guess the formula for the sum of entries for $n^{th}$ rows of Pascal’s triangle.

Answer to Problem 23WE

  $2^n$

Explanation of Solution

  

From the above figure the formula can be calculated as follows-

  $2^n$