Q. 1 B5.0( 1 Vote )

# Find the sum of the following series.162 + 172 + 18 + … + 252

Given the the series S = 162 + 172 + 18 + … + 252

Let S1 = 12 + 22 + 32 + … + 252 with n = 25

Let S2 = 12 + 22 + 32 + .. + 152 with n = 15

Required sum S = S1-S2

To find the sum S1 -

Formula to find the sum of first n squares of natural numbers is

S =

S1 =

=

S1 = 5525

To find the sum S2 -

Formula to find the sum of first n squares of natural numbers is

S =

S2 =

S2 =

S2 = 1240

Required sum S = S1-S2

S = 5525-1240 = 4285

The sum S = 162 + 172 + 18 + … + 252 = 4285

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