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

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) .