Fifth root of unity expression radical

1925SpecialistComplex NumbersAlgebra

Harvard-MIT Mathematics Tournament

Suppose $x$ is a fifth root of unity. Find, in radical form, all possible values of $$ 2x + \frac{1}{1+x} + \frac{x}{1+x^{2}} + \frac{x^{2}}{1+x^{3}} + \frac{x^{3}}{1+x^{4}}. $$

0 students attempted0% solvedRating 1925

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Fifth root of unity expression radical

1925SpecialistComplex NumbersAlgebra

Harvard-MIT Mathematics Tournament

Suppose $x$ is a fifth root of unity. Find, in radical form, all possible values of $$ 2x + \frac{1}{1+x} + \frac{x}{1+x^{2}} + \frac{x^{2}}{1+x^{3}} + \frac{x^{3}}{1+x^{4}}. $$

0 students attempted0% solvedRating 1925