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# Find the sum of the following series.

16^{3} + 17^{3} + … + 35^{3}

Answer :

Given the the series S = 16^{3} + 17^{3} + … + 35^{3}

Let S_{1} = 1^{3} + 2^{3} + 3^{3} + … + 35^{3} with n = 35

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

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

__To find the sum S _{1}__ -

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

S =

S_{1} =

=

S_{1} = 396900

__To find the sum S _{2}__ -

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

S =

S_{2} =

=

S_{2} = 14400

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

S = 396900-14400 = 382500

The sum S = 16^{3} + 17^{3} + … + 35^{3} = 382500

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