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Find the sum to 'n' terms of 1.2.3 +2.3....

Find the sum to 'n' terms of 1.2.3 +2.3.4+3.4.5+……

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`thereforeT_(n)=` (nth term of 1,2,3,… )(nth term of 2,3,4,….) (nth terms of 3,4,5…..)
`=n(n+1)(n+2)=n(n^(2)+3n+2)-n^(3)+3n^(2)+2n`
`thereforeS_(n)=sumT_(n)=sumn^(3)+3sumn^(2)+2sumn`
`=((n(n+1))/(2))^(2)+3(n(n+1)(2n+1))/(6)+2(n(n+1))/(2)`
`=[(n(n+1))/(2)]^(2)+(n(n+1)(2n+1))/(2)+n(n+1)`
`=(n(n+1))/(2)[(n(n+1))/(2)+2n+1+2]=(n(n+1))/(4)[n^(2)+n+4n+2+4]`
`=(n(n+1))/(4)[n^(2)+5n+6]=(n(n+1)(n+2)(n+3))/(4)`
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