Find the sum (2 + 4 + 6 + 8 +… + 100).
It is required to find the sum of (2 + 4 + 6 + 8 +… 100).
Now, consider the series (2 + 4 + 6 + 8 +… 100).
If we take a common factor of 2 from all the terms, then,
the series becomes,
2 (1 + 2 + 3 + 4 +… 50).
So, we need to find the sum of first 50 natural numbers.
Note:
Sum of first n natural numbers, 1 + 2 +3+…n,
From the above identities,
So, Sum of first 50 natural numbers
(2 + 4 + 6 + 8 +… 100) = 2 (1 + 2 + 3 + 4 +… 50)
= 2 x 1275 = 2550