Given that 1 = 1, 1 + 2 = 3, 1 + 2 + 3 = 6, and 1 + 2 + 3 + 4 = 10, what is the sum of the numbers from 1 to 100? Explain how you found your answer.

Extension:
What does 1 + 2 + 3 + 4 + 5 + 6 + . . . + n equal? Give your answer in terms of n. Explain your solution.