The Infinite Series $x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+\ldots+\frac{(-1)^{n-1} x^{n}}{n}+\ldots$ Does Not Converge For $x=-1$ What Behavior Does It Exhibit? It Does Converge For x=-1

question 60

Multiple Choice

The infinite series $x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+\ldots+\frac{(-1) ^{n-1} x^{n}}{n}+\ldots$ does not converge for $x=-1$ .What behavior does it exhibit? It does converge for $x=1$ .To what number does it appear to converge?

• A)At -1, the series diverges to \(\infty\) , At 1, it appears to converge to ln(3).
• B)At -1 the series diverges because the terms alternate back and forth between positive and negative.At 1, it appears to converge to ln(2).
• C)At -1, the series diverges because some of the terms are undefined.At 1, it appears to converge to ln(3).
• D)At -1, the series diverges to \(-\infty\) .At 1, it appears to converge to ln(2).

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