cubes summation

Algebra Level 1

1^3 + 2^3 + 3^3 + ...... + 8^3 = x^2

find x


The answer is 36.

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1 solution

Nihar Mahajan
Dec 24, 2014

sum of cubes from 1 to n = [n(n+1) / 2 ]^2

so , x = n(n+1) / 2

here , n = 8 so ,

x= 8 * 9 / 2

x = 36

note that here finding 'x' was same as finding sum of nos. from 1 to 8 .

so , this problem must be called as sum of natural numbers !!

we can give the proof for the sum of cubes by writing in format-

(a+1)^4 - a^4 and summation using telescopic sums

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