Sum of the first 100 positive even numbers?

Answer 1

The sum of the first 100 numbers is 5050. The sum of the first 100 even numbers is twice that, so it is 10100 Here is why. Look at the sum of the first 5 numbers, write them as 1 2 3 4 5 and then write them as 5 4 3 2 1 and write the two rows on top of each other. We 5+1 and 4+2 and 3+3 etc. So we have 5 six's and the sum is 5x6, but we wrote them twice, so divide by 2 so the sum is 5X6/2=15 as as we see just by adding them. 1+2+3+4+5=15, Now, look at the first 5 even numbers, 2,4,6,8,10= 30 which is 2 times the first 5 numbers. If we wrote them the same way we wrote the first 5 numbers we have two rows 2,4,6,8,10 and second row 10,,8,6,4,2. We have 5 ( 12)=60, but we counted each number twice, so 60/2=20

Answer 2

10,100

Answer 3

2,550