Series Estimation: Estimating Terms Needed to Reach |Error|<0.001

[fsm]

Homework Statement

$$\sum\frac{(-1)^{x}}{x*\sqrt{x}}$$

How many terms must be added to get an esimate with an |error|<0.001?

Homework Equations

$$s_n+ \int f(x)dx \leq s \leq s_n+ \int f(x)dx$$

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.

 

[fsm]

anyone?

 

[NateTG]

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

 

[HallsofIvy]

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.

 

[fsm]

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