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# Find the sum of the following series.

16^{2} + 17^{2} + 18 + … + 25^{2}

Answer :

Given the the series S = 16^{2} + 17^{2} + 18 + … + 25^{2}

Let S_{1} = 1^{2} + 2^{2} + 3^{2} + … + 25^{2} with n = 25

Let S_{2} = 1^{2} + 2^{2} + 3^{2} + .. + 15^{2} with n = 15

Required sum S = S_{1}-S_{2}

__To find the sum S _{1}__ -

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

S =

S_{1} =

=

S_{1} = 5525

__To find the sum S _{2}__ -

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

S =

S_{2} =

S_{2} =

S_{2} = 1240

Required sum S = S_{1}-S_{2}

S = 5525-1240 = 4285

The sum S = 16^{2} + 17^{2} + 18 + … + 25^{2} = 4285

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