Series Summation

Algebra Level 2

Find the sum of the series 31^3+32^3+....50^3.


The answer is 1409400.

Sudipan Mallick by Sudipan Mallick , 25, India

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2 solutions

William Isoroku
Aug 29, 2014

Use the power sum formula for cubes to find the sum of the first 50 cubes then take away the sum of the first 30 cubes.

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Sudipan Mallick
May 19, 2014

let S=(1^3+2^3+3^3+........50^3)-(1^3+2^3+3^3......30^3) =((50 x 51)/2)^2 - ((30 x 31)/2)^2 {using summation n^3=((n(n+1)/2)^2}. 1/4(50 x 51-30 x 31)(50 x 51+30 x 31) =1409400

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Yes, I did it in exactly the same way. Nice problem; it's cool how the summation of cubes from 1 to n 3 n^3 is T n 2 T_n^2 .

Michael Ng - 7 years ago

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thanks!! :)

Sudipan Mallick - 7 years ago

I did the same way.

But, can anyone prove all these types of summations?

Kartik Sharma - 7 years ago

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