h3 - n term if possible That is your answer may look like...

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[30] Homework 3. Programming Assignment: Numerical Evaluation of Certain Sums The goal of this assignment is to Fnd good numerical approximations to certain sums. We need Frst a few deFnitions. ±or nonnegative integers 0 k n deFne p n k P = n ! k !( n - k )! where n ! = 1 · 2 ··· n . [15] Stirling’s Approximation : Tabulate and plot I n = n s k =1 ln k for a range of n (e.g., 1 n 500). Based on this numerical computation Fnd a good a approximation formula for ln n ! = n s k =1 ln k for large n up to a log
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Unformatted text preview: n term, if possible. That is, your answer may look like this log n ! ≈ ? n 2 log n + n + 3 log n. Plot your approximation on the same graph as I n . [15] An Interesting Sum : Tabulate and plot S n = n s k =1 p n k P 2-n log 2 p n k P for 1 ≤ n ≤ 500. Based on this numerical computation Fnd a good approximation of S n for large n , as in the previous case, and plot it together with S n . 1...
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