Question

Find the sum of the following series to `n` term: `3xx1^2+5xx2^2+7xx3^2+`

Answer 1

Correct Answer - `(n(n+1)(3n^(2)+5n+1))/(6)`
`T_(n)=("nth tem of "3,5,7,..) xx ("nth term of "1^(2),2^(2),3^(2),...)`
`={3+(n-1)xx2}xx n^(2)=(2n+1)n^(2)=(2n^(3)+n^(2)).`
`therefore S_(n)=2(sum_(k=1)^(n)k^(3))+(sum_(k=1)^(n)k^(2)).`