Need help with the following questions:

Write down the answers to the following questions. I do not want references to some mathematical theorem. I want your own easy to understand explanations that would make sense even to 8 year olds.

1. We have learned that Sum of K as K varies from 1 to N is 1+2+3++N = N(N+1) /2

Why do *you* think it is N(N+1) /2 ? Explain. (Hint: draw bar graphs within a rectangle)

2. We have learned that there are N(N-1) /2 pairs when you have N elements.

Why do *you* think it is N(N-1) /2 ? Explain. (Hint: draw dots and pair them up with lines)

3. We have learned that there are A^N ways to assign one of A values to each of the N people.

Why do *you* think it is A^N? Explain.