Find the sum of `n` terms of the series `1. 2. 3+2. 3. 4+3. 4. 5+ `

Explanation

Here, `T_(n)={" nth term of " 1,2,3,"....""}`
`xx={" nth term of " 2,3,4,"...."}xx={" nth term of " 2,3,4,"...."}`
` therefore T_(n)= n(n+1)(n+2)=n^(3)+3n^(2)+2n`
` therefore S_(n)= " Sum of n terms of the series "`
`sum T_(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)+{(n(n+1))/(2)+(2n+1)+2}`
`=(n(n+1))/(4)(n^(2)+n+4n+2+4)`
`=(n(n+1)(n+2)(n+3))/(4)`