Find the sum of n terms of the series when nth terms is :
`(i)n^(2)+n" "(ii)n^(2)+2^(n)`

Answer

N/a

Explanation

(i) `T_(n)=n^(2)+n`
`rArr" "S_(n)=Sigma(n^(2)+n)=Sigman^(2)+Sigman`
`=(1)/(6)n(n+1)(2n+1)+(1)/(2)n(n+1)`
`=(n(n+1)(2n+1)+3n(n+1))/(6)`
`=(1)/(6)n(n+1)(2n+1+3)`
`=(1)/(6)n(n+1)(2n+4)`
`=(1)/(3)n(n+1)(n+2).`
(ii) `T_(n)=n^(2)+2^(n)`
`rArr" "S_(n)=Sigma(n^(2)+2^(n))=Sigman^(2)+Sigma2^(n)`
`=(1)/(6)n(n+1)(2n+1)+(2+2^(2)+2^(3)+...+2^(n))`
`=(1)/(6)n(n+1)(2n+1)+(2(2^(n)-1))/(2-1)`
`(1)/(6)n(n+1)(2n+1)+2(2^(n)-1)`.