Math Help - Alternating Series Estimation Theorem

Use the alternating series estimation theorem to approximate the sum of from n=0 to infinity with an error of .

I know that after summing a number of terms, the remainder(error) will be less than the first omitted term, so

I've set up the problem like this:



Is this right, and if so, what's next?

Originally Posted by JewelsofHearts

Use the alternating series estimation theorem to approximate the sum of from n=0 to infinity with an error of .

I know that after summing a number of terms, the remainder(error) will be less than the first omitted term, so

I've set up the problem like this:



Is this right, and if so, what's next?

So you want the least integer such that:



To proceed you need either to use trial and error or some suitable approximation for the factorial (and then a numerical solution of the resulting equation).

(look up and )

CB

Shouldn't it be (n+1)!<200000?

Originally Posted by JewelsofHearts

Shouldn't it be (n+1)!<200000?

Probably counting zeros is not something I am particularly careful about

Not only the zeros, but I think the direction of the inequality sign is supposed to be different. I really don't know, though. I don't understand the theorem.

Help, please!

error,



note the following factorial values ...





so, how many terms of the series would you need to add to get an error less than ?

fyi, to check your work, note ...