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Find the sum of the series 31^3+32^3++50...

Find the sum of the series `31^3+32^3++50^3dot`

Text Solution

Verified by Experts

The correct Answer is:
1409400
`S=(1^(3)+2^(3)+..+50^(3))-(1^(3)+2^(3)+…+30^(3))`
`=((50xx51)/2)^(2)-((30xx31)/2)^(2)` [Using `Sigman^(3)=((n(n+1))/2)^(2)]`
`=1/4(50xx51-30xx31)(50xx51+30xx31)`
=1409400
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