Consider a $10 \times 10$ checkerboard, consisting of 100 squares. How many squares exist that are the union of one or more squares of the checkerboard?
Answer: 385. There is 1 square $10 \times 10, 4$ squares $9 \times 9, \ldots$ so the answer is $1+2^{2}+3^{2}+\cdots+10^{2}=385$.