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If sum(r=1)^n r=55 ,find sum(r=1)^n r^3....

If `sum_(r=1)^n r=55` ,find `sum_(r=1)^n r^3.`

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Verified by Experts

As given `sum_(r=1)^n r=55`
We have to find `sum_(r=1)^n r^3.`
Then
`sum_(r=1)^n r^3=1^3+2^3+3^3+..........+n^3`
`sum_(r=1)^n r^3=[(n(n+1))/2]^2`
`sum_(r=1)^n r^3=[sum_(r=1)^n r]^2`
`sum_(r=1)^n r^3=55^2`
`sum_(r=1)^n r^3=3025`
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