Question

Let R₁ and R₂ be the radii of convergence of the power series \(\sum\limits_{n=1}^{\infin}(-1)^nx^{n-1}\) and \(\sum\limits_{n=1}^{\infin}(-1)^n\frac{x^{n+1}}{n(n+1)}\), respectively. Then

• A. R₁ = R₂
• B. R₂ > 1
• C. \(\sum\limits_{n=1}^{\infin}(-1)^nx^{n-1}\) converges for all x ∈ [−1, 1]
• D. \(\sum\limits_{n=1}^{\infin}(-1)^n\frac{x^{n+1}}{n(n+1)}\) converges for all x ∈ [−1, 1]

Answer 1

The Correct Option is A, D

The correct option is (A) : R₁ = R₂ and (D) : \(\sum\limits_{n=1}^{\infin}(-1)^n\frac{x^{n+1}}{n(n+1)}\) converges for all x ∈ [−1, 1].