Question

How do you do this question with the given power series?

Answer 1

Explanation:

tan⁻¹(x) = ∑ₙ₌₀°° (-1)ⁿ x²ⁿ⁺¹ / (2n+1)

tan⁻¹(1/√3) = ∑ₙ₌₀°° (-1)ⁿ (1/√3)²ⁿ⁺¹ / (2n+1)

tan⁻¹(1/√3) = ∑ₙ₌₀°° (-1)ⁿ (1/√3) (1/√3)²ⁿ / (2n+1)

tan⁻¹(1/√3) = (1/√3) ∑ₙ₌₀°° (-1)ⁿ (1/3)ⁿ / (2n+1)

π/6 = (1/√3) ∑ₙ₌₀°° (-1)ⁿ (1/3)ⁿ / (2n+1)

π = (6/√3) ∑ₙ₌₀°° (-1)ⁿ (1/3)ⁿ / (2n+1)

π = 2√3 ∑ₙ₌₀°° (-1)ⁿ / (3ⁿ (2n+1))