# Thread: Alternating Series Estimation within certain error

1. ## Alternating Series Estimation within certain error

Hi guys, I'm doing a few problems for my homework assignment where I am given three alternating series and first asked to decide whether the conditions of the alternating series test is satisfied for which I have accomplished however the latter part of the question asks to do an alternating series estimation and I'm having trouble understand what's going on. Attached is an image of the problem and part B is where I'm having trouble. Can someone help me understand how I can quickly out how many terms I would need in order to reach 10-8 of the series?

2. ## Re: Alternating Series Estimation within certain error

Originally Posted by AltamashMomin
Hi guys, I'm doing a few problems for my homework assignment where I am given three alternating series and first asked to decide whether the conditions of the alternating series test is satisfied for which I have accomplished however the latter part of the question asks to do an alternating series estimation and I'm having trouble understand what's going on. Attached is an image of the problem and part B is where I'm having trouble. Can someone help me understand how I can quickly out how many terms I would need in order to reach 10-8 of the series?
I hope you were careful with Monotonicity on the second series.

If $\sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{a_n}} = S$ then it can be approximated $\left| {{S_n} - S} \right| \leqslant {a_{n + 1}}$