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Find the sum of n terms of the series wh...

Find the sum of n terms of the series whose nth terms is
(i) `n(n-1)(n+1)`.

Text Solution

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(i) We have, `T_(n)=n(n-1)(n+1)=n^(3)-n`
` therefore " sum of n terms " S_(n)= sumT_(n)`
`2=sumn^(3)+2sumn^(2)+sumn`
`={(n(n+1))/(2)}^(2)-{(n(n+1))/(2)}`
`=(n(n+1))/(2)-{(n(n+1))/(2)-1}`
`=(n(n+1)(2)(n-1)(n+2))/(4)`
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