Alternating Series Approximation

[bcjochim07]

Homework Statement

Determine the number of terms required to approximate the sum of the series with an error of less than .001

Sum ((-1)^(n+1))/(n^3) from n=1 to infinity

Homework Equations

The Attempt at a Solution

I guess this is what you do

1/(n+1)^3 < 1/1000

and solving you get n+1 > 10 so 10 terms

But that doesn't quite make sense to me, and I'm not sure why.

Alternating series remainder theorem:

|S-Sn| =|Rn|< or = to an+1

Could someone please explain this to me?

 

[Gib Z]

Ok so basically all the inequality is working out "From which point do the terms i add on become less significant than 0.001" which also answers the original question. Then you solved that inequality to see that they become less significant that 0.001 when n> 9. Thats all it means.

 

[HallsofIvy]

Since this is an alternating series, each partial sum is BETWEEN the two previous sums. Yes, If you find a value of n such that the difference between two consecutive sums (which is just the value of the n th term) is less than 0.001, you know the error will be less than that.