Find the sum of the following series.

2 + 4 + 6 + … + 100

Given the series S = 2 + 4 + 6 + … + 100,

We see that there is a common term 2 in all the numbers in the series. Taking 2 common, we have

S = 2(1 + 2 + 3 + .. + 50)

Let 1 + 2 + 3 + .. + 50 be S₁, with n = 50

S = 2S₁

To find S₁ -

Formula for sum of first n numbers is

S₁ =

25x51

= 1275

S = 2S₁

= 2 × 1275 = 2550

S = 2550

The sum S = 2 + 4 + 6 + … + 100 = 2550