Geometric verification

number theory

I just started to read "Friendly Introduction to Number Theory". Now I'm trying
exercises 1-2

1.2. Try adding up the first few odd numbers and see if the numbers you get satisfy some sort of pattern. Once you find the pattern,
express it as a formula. Give a geometric verification that your
formula is correct.

https://www.math.brown.edu/~jhs/frintch1ch6.pdf

I think the pattern is Σ[n=0..n](2*n + 1)

But what is geometric verification? How should I answer this question?

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Best Answer

For one odd you get $1$ which is presented by a red square.

For tow odds you get $1+3$ which is presented by one red square and three yellow square and together they make a $2\times 2$ square.

You are supposed to find out that when you keep adding odd numbers you will get a square for the sum.

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