h3-sol

# h3-sol - log(log log 2 1 log log 1 n e n n n n k n k −...

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Solution of Homework 3 ** Note that the approximate functions shown below are not unique and are provided for the sake of illustration not perfection. Prob.1 02 . 0 1 2 ) 2 ( 2 3 1 n k H n k n = = Algorithm H(1) =1 for k = 2 to n H(k) = H(k-1) + 1/k^2 n exact approximation 1 1 1.5 50 1.625132734 1.622073985 100 1.6349839 1.644717294 150 1.638289573 1.658109029 200 1.639946546 1.667676692 250 1.640942056 1.675135951 300 1.641606283 1.681255369 350 1.642081002 1.6864467 400 1.642437189 1.690956591 450 1.642714312 1.694944606 500 1.642936066 1.698519977 550 1.643117537 1.70176079 600 1.643268788 1.704724819 650 1.643396788 1.70745602 700 1.643506515 1.709988619 750 1.643601622 1.712349788 800 1.643684848 1.714561465 850 1.643758288 1.716641619 900 1.643823573 1.718605151 950 1.643881989 1.720464561 1000 1.643934567 1.722230432

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Solution of Homework 3 Approximation of the Harmonic Numbers 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 100 200 300 400 500 n Exact Approximation
Solution of Homework 3 Prob. 2 Using Stirling’s formula: π n e n n n 2 ! ) 2 log( 5 . 0 )

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Unformatted text preview: log (log ! log ) ... 2 1 log( log 1 n e n n n n k n k + − ≈ = × × × = ∑ = Algorithm S(1) = 0 for k = 2 to n S(k) = S(k-1) + ln(k) n exact approximation 1-0.035117164 50 64.48307487 64.48243844 100 157.9700037 157.9697291 150 262.7568934 262.7567395 200 374.8968886 374.8967951 250 492.5095864 492.509529 300 614.485803 614.4857698 350 740.0919742 740.0919582 400 868.8064142 868.8064111 450 1000.238891 1000.238898 500 1134.086409 1134.086424 550 1270.106851 1270.106873 600 1408.102287 1408.102314 650 1547.907871 1547.907903 700 1689.384181 1689.384217 750 1832.411755 1832.411794 800 1976.887084 1976.887126 850 2122.719619 2122.719664 900 2269.829476 2269.829523 950 2418.145657 2418.145706 1000 2567.604644 2567.604695 Solution of Homework 3 Stirling's Approximation 500 1000 1500 2000 2500 3000 100 200 300 400 500 600 700 800 900 1000 n Exact Approximation...
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h3-sol - log(log log 2 1 log log 1 n e n n n n k n k −...

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