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.