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
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
Updated On: Oct 1, 2024
- R1 = R2
- R2 > 1
- \(\sum\limits_{n=1}^{\infin}(-1)^nx^{n-1}\) converges for all x ∈ [−1, 1]
- \(\sum\limits_{n=1}^{\infin}(-1)^n\frac{x^{n+1}}{n(n+1)}\) converges for all x ∈ [−1, 1]
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The Correct Option is A, D
Solution and Explanation
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].
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