Be sure that diagram accounts for the first three square numbers

Question

Draw a diagram that illustrates the fact that the sum of the first n odd natural numbers or the sum of the first n odd positive intergers is a square number.

Answer 1

Step 1:

The sum of the first odd natural numbers is a square number.

Draw the diagram for the first three square numbers.

First three odd numbers are .

In the diagram blue colour dot represents and pink colour dot represents and green colour dot represents .

Observe the diagram:

Sum of  .

.

.

Solution:

The sum of the first odd natural numbers is a square number.