Alice sums \(n\) consecutive numbers, not necessarily starting from \(1\), where \(n\) is a multiple of four. An example of such a sum is \(5+6+7+8\). Can this sum ever be odd?
Show that the difference between two consecutive square numbers is always odd.
One of the most powerful ideas in mathematics is that we can make symbols or letters — like \(a,b,c\) or \(n\) - stand for numbers, shapes, or other objects. When we do this, we can reason about all of them at once, without for example knowing exactly which numbers they really are. As long as we follow the same rules that numbers follow, our reasoning will always stay true. Today we will practice this skill of reasoning with such symbols. We call this style of reasoning algebra.