Using the power series for ln(x + 1) and the Estimation Theorem for the Alternating Series, we conclude that the least number of terms in the series needed to approximate ln 2 with error < 3/1000 is: (i) 333 (ii) 534 (iii) 100 (iv) 9 (v) 201
ln(x+1) = Σ(-1)^nx^n/n!
The Attempt at a Solution
I know that the alternating series estimation thm is |Sn-S| ≤ (estimation) which is 3/1000. I get x to be equal to 1 since we want ln(2), but when I setup the equation I get lost on how to simplify this to a specific n value. (Calculators are not allowed on exam so I am rusty with algebra).
I get (-1)^n+1 * 2^n/(n+1)! ≤ 3/1000 which gives 2^n ≤ 3/1000 * (n+1) and I can't figure how to get the n in the exponent down without using ln yet the answers are specific numbers.