Step 1:

\

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

\

Draw the diagram for the first three square numbers.

\

First odd numbers are \"\".

\

In the diagram blue colour dot represent \"\" and pink colour dot represent \"\" and green colour dot represent \"\".

\

 

\

\

Observe the diagram:

\

Sum of  \"\"\"\".

\

\"\"\"\".

\

\"\"\"\".

\

Step 2:

\

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

\

Need to prove \"\".

\

Odd natural numbers are \"\".

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\"\"Sum of the first \"\" odd natural numbers\"\"
\"\"\"\"\"\"
\"\"\"\" \

\"\"

\
\"\"\"\" \

\"\"

\
\

\"\"

\
\"\"\"\"
\

\"\"

\
\"\"\"\"
\"\"\"\"\"\"
\

\"\"

\
\"\"\"\"
\

\"\"

\

\"\"

\

\"\"

\

\"\"

\

\"\"

\

\"\"

\

\"\".