Can you explain the sum of 1 to 100?

The idea here is to pair your numbers up to get to the solution. If you were to put this through a calculator it would take you a while. However, if we simplify the problem to the sum of 1 to 10 you'll be able to check your answer on the calculator.Get your calculator out and do 1+2+3+4+5+6+7+8+9+10. What did you get? (Sum=55) Now, how can we do this without a calculator? Like I said before, the idea is to pair them up. If I tell you that you could pair 1 and 10, what's 1+10? What could the next pair be? 2+9= ? What is the pattern? How many 11's did you get? So have you found the sum in a simple way?
Now try the same trick with 1+2+3+4+ ... + 97+98+99+100. 1+100= ?, 2+99=?, 3+98=? But how many would you get? Think about what would happen in the middle ..... +47+48+49+50+51+52+53+54+... which ones pair up? So how many do you have? And what's the answer? You should have got 5050.