Question

Hi I would like to know how I can solve this problem.

Answer 1

The
`n`-th term is

`U_n = \frac14 n^2 (n+1)^2`

so the 39th term is

`U_(39) = \frac14 39^2 40^2 = \boxed{608,400}`

Observe that

`2^3 + 4^3 + 6^3 = 2^3 + 2^3*2^3 + 2^3*3^3 = 8\left(1^3+2^3+3^3)`

which suggests that

`V_n = 8U_n = \boxed{2n^2(n+1)^2}`