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 ?
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! )
you won't have such a problem in your exam then! haha
because is always the 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
And why is it and not ?
positive, decreasing and then for any