In Prob. 26 Using e x < e (0 < x < 1), conclude that |I n

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In Prob. 26 Using ex < e (0 < x < 1), conclude that |In| ≤ e/(n + 1) → 0 as n → ∞. Solve the iteration formula for In-1 = (e - In)/n, start from I15 ≈ 0 and compute 4S values of I14, I13, · · ·, I1.

Data from Prob. 26

Integrating by parts, show that In = ∫10 exxn dx = e -nIn-1, I0 = e - 1.

(a) Compute In, n = 0, · · ·, using 4S arithmetic, obtaining I8 = -3.906. Why is this nonsense? Why is the error so large?

(b) Experiment in (a) with the number of digits k > 4. As you increase k, will the first negative value n = N occur earlier or later? Find an empirical formula for N = N(k)

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