is the series Σ[(√n³+1)⁽¹÷³⁾-n] convergent or divergent?

Question

which test i should follow to solve the problem?

Answer 1

Use the comparison test

Σ[(n³+1)^1/3-n] = ∑1/[(n³+1)^2/3 + (n³+1)^1/3n + n²]

                       < ∑1/n²=pi²/6

 

a - b = (a³ - b³) / (a² + ab + b²)