**Unformatted text preview: **≤ 2, so we can use the series to represent ln( x ) when 0 < x ≤ 2. For example ln(3 / 2) = ln(1- -1 / 2) = ∞ X n =0 (-1) n 1 n + 1 1 2 n +1 and so ln(3 / 2) ≈ 1 2-1 8 + 1 24-1 64 + 1 160-1 384 + 1 896 = 909 2240 ≈ . 406 . Because this is an alternating series with decreasing terms, we know that the true value is between 909 / 2240 and 909 / 2240-1 / 2048 = 29053 / 71680 ≈ . 4053, so correct to two decimal places the value is 0 . 41....

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- Fall '07
- JonathanRogawski
- Math, Calculus, Polynomials, Infinite Series, Power Series, Sequences And Series, Mathematical Series, n=0