Find the sum (2 +

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