1. Nov 13, 2004

### kdinser

Again, my rusty algebra and derivative taking is getting me into trouble.

This is from the section on alternating series. Overall, I think I'm getting the concepts, but some of the solutions to the problems are leaving me scratching my head.

$$\sum \frac{(-1)^{n+1}(n+1)}{ln(n+1)}$$

How did the solutions manual go from:

$$\lim_{n\rightarrow \infty}\frac{(-1)^{n+1}(n+1)}{ln(n+1)}$$

to this?
$$\lim_{n\rightarrow \infty}\frac{1}{1/(n+1)}$$

If someone could just tell me what concept they are using to rearrange this, I'd happily go look it up myself. I dug through my old algebra book and a second calc book and can't find anything like this.

Another problem that I'm having this morning is with an example problem in the same chapter.

They are applying L'Hopital's Rule to test for convergence

$$\lim_{n\rightarrow \infty}\frac{x}{2^{x-1}}$$

Again, looking back through past chapters, I can't find a single example of how to take the derivative of
$$2^{x-1}$$

I think I'm just forgetting something obvious here.

2. Nov 13, 2004

### Staff: Mentor

$$\frac{d}{dx} (a^x) = a^x ln(a)$$