The sum of all even integers between 1 and 101 is 2550.
Here's a breakdown of how we arrive at this answer:
We need to sum the even numbers from 2 to 100. This can be represented as:
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 determine the number of terms (n). The formula for the nth term is: a + (n-1)d = l.
So, 2 + (n-1)2 = 100. Solving for n, we get:
2 + 2n - 2 = 100
2n = 100
n = 50
Therefore there are 50 terms in the series.
Now, we can find the sum using the arithmetic series sum formula, S = n/2 * (a+l):
S = 50/2 (2 + 100)
S = 25 102
S = 2550
Therefore, the sum of even integers from 1 to 101, which is equivalent to the sum of even integers from 2 to 100, is 2550, as provided in the reference.
