ren6989 ren6989
  • 23-07-2022
  • Mathematics
contestada

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

Hi I would like to know how I can solve this problem class=

Respuesta :

LammettHash
LammettHash LammettHash
  • 23-07-2022

The [tex]n[/tex]-th term is

[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]

so the 39th term is

[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]

Observe that

[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]

which suggests that

[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]

Answer Link

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