1. ## power series?

Man, this class is horrible. I just got a 56 on the midterm and it was one of the top scores in the class since the average is a 40. The book is so unhelpful...they give us some general examples and theories and then bombard us with dozens of questions far more advanced than any of the info they give us. Anyway, enough of a rant, onto my question. I am working on a similar problem to this one. I understand how they get the derivative but have no idea how they go from there to the final solution. This is from our solutions manual which gives us the odd-numbered answers. The step I don't understand is followed by ???.

2. Originally Posted by CrazyLond
Man, this class is horrible. I just got a 56 on the midterm and it was one of the top scores in the class since the average is a 40. The book is so unhelpful...they give us some general examples and theories and then bombard us with dozens of questions far more advanced than any of the info they give us. Anyway, enough of a rant, onto my question. I am working on a similar problem to this one. I understand how they get the derivative but have no idea how they go from there to the final solution. This is from our solutions manual which gives us the odd-numbered answers. The step I don't understand is followed by ???.

WEll first off there is a problem

The index should read $\sum_{{n=\color{red}{1}}}^{{\infty}}(-1)^nnx^{n-1}$

Then adjusting that down to zero we get,

$\sum_{n=0}^{\infty}(-1)^{n+1}(n+1)x^{n}$

This was just gotten through elementary index manipluation

Now then using the root test we get the interval of convergence is equal to

$\lim_{n\to\infty}|(n+1)x^n|^{\frac{1}{n}}<1\Righta rrow|x|<1$

Now putting in both x=1 and x=-1 we get divergence by the n-th term test

3. I guess I'm weak on index manipulation.

Looking closer, n=1 is what they had there. Why does it go from 0 to 1 in the first place? I guess I'll review the chapter on those things.

4. Originally Posted by CrazyLond
I guess I'm weak on index manipulation.

Looking closer, n=1 is what they had there. Why does it go from 0 to 1 in the first place? I guess I'll review the chapter on those things.
You tell me, look at the exponent of the x term in the power series, and report back

5. I guess we don't want a negative exponent? I guess that makes sense, thanks.