cube

Algebra Level 3

1 3 2 3 + 3 3 4 3 . . . . . . . . . . . . . . . . . . . . . . . . . + 9 9 3 1^3-2^3+3^3-4^3.........................+99^3


The answer is 492500.

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2 solutions

Saya Suka
May 20, 2019

Use [n(n+1)/2]^2 for cubic summations.
Answer = [99 * 100 / 2]^2 - 2 * 2^3 * [49 * 50 / 2]^2.
= (99 x 50)^2 - 4(49 x 50)^2.
= 50^2 (99^2 - 98^2).
= (99 - 98)(99 + 98)50^2.
= 197 x 2500.
= 492500


Rajas Samel
Jan 10, 2015

It's gonna be tough to write since I dunno latex.. I tried simplifying it.. Summation (n=1 to 99) = (-1)^(n+1) × n^3.

If any better solution please reply me down there..!

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