Q. 1 C

# 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

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