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# Find the sum of t

Given the the series S = 163 + 173 + … + 353

Let S1 = 13 + 23 + 33 + … + 353 with n = 35

Let S2 = 13 + 23 + 33 + .. + 153 with n = 15

Required sum S = S1-S2

To find the sum S1 -

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

S =  S1 = = S1 = 396900

To find the sum S2 -

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

S =  S2 = = S2 = 14400

Required sum S = S1-S2

S = 396900-14400 = 382500 The sum S = 163 + 173 + … + 353 = 382500

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