What is the sum of the first one hundred counting number?

Answer 1

Here is a nice way to see and remember this. Look at the sum of the first 5 counting number Write them as 1,2,3,4,5 Now write them backward as 5,4,3,2,1 Place the second list under the first list and add the numbers in each column. Each sum is 6 and there are 5 sums. However, you counted the numbers twice since you wrote the list both ways. So the sum of the first 5 numbers is 5x6/2 In general the sum of the first n natural numbers is n(n+1)/2 So the sum of the first 100 numbers is 100x101/2=50x101=5050 This formula can also be proved by induction and several other ways.