Question

Pascal’s Triangle: Divide the triangular array shown (called

Pascal’s triangle) using diagonal lines as indicated. Find the

sum of the numbers in each of these diagonal rows. Do you

recognize this sequence?

Short answer

The given sequence is a Fibonacci series.

Step-by-step solution

Step 1. Write the given information.

Given the Pascal's Triangle in which as shown in the picture, numbers have to be added that fall in the same diagonal row.

Step 2. Add the numbers in the same diagonal row.

Adding the numbers give:

Row 1: 1

Row 2: 1

Row 3: 1+1=2

Row 4: 1+2=3

....

Following table shows the results as:

Observe the sum of numbers obtained.

The series formed from the sum of numbers in the same diagonal row is the Fibonacci series.