Problema Solution
what is the sum of the even numbers from 1 to 100?
Answer provided by our tutors
The event numbers from 1 to 100 are: 2, 4, 6, 8, ... 100.
We need to find:
2 + 4 + ... + 100 = 2(1 + 2 + 3 + ... + 50)
We know that the sum of the first consecutive n numbers is: (1/2)n(n + 1)
We use the above formula to find:
1 + 2 + ... + 50 = (1/2)50*(50 + 1) = 25*51
We used the fact that n = 50 and we plugged the value into the formula.
Now we can write:
2(1 + 2 + 3 + ... + 50) = 2*25*51
That is:
2 + 4 + ... + 100 = 2*25*51 = 50*51 = 2550
The sum of the even numbers from 1 to 100 is 2550.