Q. 1 B5.0( 1 Vote )

Find the sum of the following series.

162 + 172 + 18 + … + 252

Answer :

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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