Everything is correct but for the last step.
You want (not "=") and that gives, just as you say, .
Then n= 4, not 3.
I am having problems understanding Alternating Series Estimation Theorem...
For the 2nd half of the question (finding the natural number of n)... (ignore the equal signs, I was getting desperate), I thought that like the other tests like convergence, limit comparison, etc that
with the error being the 0.004?
But that is apparently wrong. I double checked my algebra and it is correct... so it is just a signage error.
If anybody could even give a hint, that would be greatly appreciated... this whole chapter on series and sequences is confusing.
Thanks a bunch?