Find the sum of the series ` 1 . 3^(2) + 2.5 ^(2) + 3.7^(2) +…+ ` to n terms

Explanation

`n^(th) "term " = (n^(th) "term of 1, 2, 3, "….)xx(n^(th) "term of " 3^(2) , 5^(2), 7^(2),…)`
` = n(2n +1)^(2)`
`= n(4n^(2) + 4n +1)`
`= 4n^(3) + 4n^(2) = n`
Required sum ` = 4 sumn^(3) + 4 sum n^(2) + sum n`
` = 4 [(n(n+1))/(2)]^(2) +4 .(n( +1)(2n+1))/(6)+(n(n+1))/(2)`.