Q. 1 C

Find the sum of the following series.

2 + 4 + 6 + + 100

Answer :

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


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