Find the sum `{(6)^(3)+(7)^(3)+(8)^(3)+(9)^(3)+(10)^(3)}.`

1.	Find the sum `{(6)^(3)+(7)^(3)+(8)^(3)+(9)^(3)+(10)^(3)}.`
Answer» Correct Answer - 2800 We know that `(1^(3)+2^(3)+3^(3)+ ...+n^(3))={(1)/(2)n(n+1)}^(2).` `therefore " given sum"={1^(3)+2^(3)+3^(3)+4^(3)+5^(3)+6^(3)+...+(10)^(3)}-{1^(3)+2^(3)+3^(3)+4^(3)+5^(3)}` `=((1)/(2)xx10xx11)^(2)-((1)/(2)xx5xx6)^(2)=(55)^(2)-(15)^(2)=(3025-225)=2800.`

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