**Problem 6:**

Consider the given diagram. There are three rectangles shown here. Their lengths are $3,\ 4$ and $5$ units respectively, widths respectively $2,\ 3$ and $4$ units. Each small grid represents a square $1$ unit long and $1$ unit wide. Use these diagrams to find out the sum of the consecutive numbers from $1$ to $500$. (If you use some direct formula for doing so, you must provide its proof)