The sum of the positive even integers from 1 to 100 is 2550.
Let's break down how to arrive at this answer. We're looking to sum the series:
2 + 4 + 6 + ... + 100
This is an arithmetic series where:
- The first term (a) is 2.
- The common difference (d) is 2.
- The last term (l) is 100.
First, we need to find the number of terms (n) in the series. Since all the terms are even numbers, and range from 2 to 100, we can calculate n by dividing the last term by 2:
n = 100 / 2 = 50
Now we can use the formula for the sum of an arithmetic series:
S = (n/2) * (a + l)
Where:
- S is the sum of the series
- n is the number of terms
- a is the first term
- l is the last term
Plugging in the values:
S = (50/2) (2 + 100)
S = 25 102
S = 2550
Therefore, the sum of the positive even integers from 1 to 100 is indeed 2550.
