Understanding Consecutive Squares and Odd Numbers

The video tutorial explores the differences between consecutive squares, revealing a sequence of non-negative odd numbers. It provides a mathematical proof showing that the difference of consecutive squares results in an odd number, expressed as 2n + 1. The tutorial expands and simplifies the expression to demonstrate this pattern.

What pattern emerges when subtracting consecutive squares?

• A sequence of negative numbers

• A sequence of non-negative odd numbers

• A sequence of even numbers

• A sequence of prime numbers

Which formula represents an odd number?

• 2n

• 2n + 1

• n^2

• n + 1

What is the expression for the difference of consecutive squares?

• (n+1)^2 - n^2

• n^2 - (n-1)^2

• 2n + 1

• n^2 + n

What is the result of expanding (n+1)^2?

• n^2 + 2n + 1

• n^2 + n

• 2n + 1

• n^2 - n

Why does the difference of consecutive squares always result in an odd number?

• Because n^2 is always even

• Because (n+1)^2 is always odd

• Because the expression simplifies to 2n + 1

• Because n is always odd