# Series estamation

1. Oct 7, 2007

### fsm

1. The problem statement, all variables and given/known data
$$\sum\frac{(-1)^{x}}{x*\sqrt{x}}$$

How many terms must be added to get an esimate with an |error|<0.001?
2. Relevant equations
$$s_n+ \int f(x)dx \leq s \leq s_n+ \int f(x)dx$$

3. The attempt at a solution
I having some problems trying to attempt this. To use this the function must be continuous which it is. Then it has to be positive and decreasing--this to me is the rub. The graph is symmertic at the horizontal asymptote x=0. So part of the graph is negative and increasing. I feel like I hit a brick wall. The only other thing I can think of is to rewrite the demoninator as x^(3/2), compare to a p-series and then find how many terms.

2. Oct 8, 2007

anyone?

3. Oct 8, 2007

### NateTG

There's a generic method for alternating series you can use to easily answer this question.

4. Oct 8, 2007

### HallsofIvy

Staff Emeritus
Since, as NateTG said, this is an alternating sequence, the error, after n terms can't be more than the difference between the last two terms. Plot a few terms on a number line to convince your self of this.

5. Oct 8, 2007

### fsm

Thanks everyone for the help. I thought that originally but second guessed myself. And I got the answer.