Answer :

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


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