Without actually calculating the cubes,find the value of (-1)³+ (-2)³+(-3)³+(-4)³+2(5)^3.

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Solution

1^3 + 2^3 + ....... + n^3 = [n (n+1) / 2]^2

So, (-1)^3 + (-2)^3 + (-3)^3 + (-4)^3 + 2(5)^3

= - [ 4 (4+1) / 2]^2 + 2(5)^3

= - 4(5)^2 + 2(5)(5)^2

= - 4 (5)^2 + 10 (5)^2

= 6 (5)^2

= 6(25)

= 150

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