Apply Gauss' formula n(n+1)/2

6 to 246, but only the even numbers. 246/2 means 123 even numbers 2 to 246. Subtract 2, as it doesn't include the 2 or 4, to get 121 numbers in the sequence.

6,8,10,12,14......242,244,246

divide them all by 2 to get another sequence 3,4,5,....121,122,123

This is a sequence that can be summed applying Gauss' formula n(n+1)/2

If you sum 1 through 6, here n=6, the sum is 6(7)/2=21 =1+6 +2+5 +3+4 you can group then in subgroups adding to 7

Apply Gauss' formula to 1 through 123, then subtract off 1 and 2 which aren't in the sequence

sum=123(124)/2 = 123(62) =7626 subtract 1 and 2 to get the almost final answer: 7623. Now multiply it by 2 as we wanted the sequence double what we just found: 7623x2= 15,246 feet

Gauss came up with this formula when he was about 3 years old. His teacher wanted to keep him busy for a while and told him to add up all numbers from 1 to 100. In seconds Gauss gave the correct answer, with that formula n(n+1)/2 with n=100, so the sum was 100(101)/2=50(101)=5050. it took the teacher a while to grade him on that though. And the teacher was more careful with Gauss after that. There are 50 subgroups adding up to 101, 1+100, 2+99, ...50+51

Arthur D.

02/20/14