Find smallest n so that the finite sum is certain to differ from by less than .001.

So I set up the inequality:

And that is where I am stuck. How do I solve for ?

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- May 9th 2009, 04:59 PMPinkkFinding smallest n for finite sum
Find smallest n so that the finite sum is certain to differ from by less than .001.

So I set up the inequality:

And that is where I am stuck. How do I solve for ? - May 9th 2009, 05:35 PMNonCommAlg
note that not the inequality cannot be solved for algebraically. however, it is possible to make it a little simpler by finding a lower bound for

which is not worth the effort anyway. the easiest way, and you're expected to do it this way, to use your calculator. i think you'll get (don't trust my calculations! do it yourself! (Nod)) - May 9th 2009, 05:40 PMPinkk
We're not allowed to use calculators for any of our exams, so my professor must have accidentally entered this problem. And why is it and not ?

- May 9th 2009, 06:04 PMNonCommAlg
you won't have such a problem in your exam then! haha

Quote:

And why is it and not ?

__absolute value__of the n-th term of your alternating series. the theorem that they taught you, and you should take a look at it again, is that if the sequence is

positive, decreasing and then for any - May 9th 2009, 06:10 PMPinkk
Ah, okay, I get it. Thanks!