Let T=k=1∑∞(−1)kekk.
Student C truncates the series after the third term, reporting P3. Student D truncates after the fifth term, reporting P5. Each student records all calculations to eight decimal places.
(a) Show that the terms ak=(−1)kekk satisfy the necessary conditions for convergence of an alternating series.
(b) Establish an upper bound for ∣T−P3∣.
(c) Establish an upper bound for ∣T−P5∣.
(d) Suppose a hand-held calculator requires 0.04 seconds to evaluate each individual term. Using your results from parts (b) and (c), determine which student attains the smaller maximum possible error per second of computation. Justify your answer quantitatively.