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April 17th, 2013, 01:22 PM   #1
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Estimate the value of this sum...

[attachment=0:2nevj4vn]Logic1.png[/attachment:2nevj4vn]

Where do I start on this one?
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 April 17th, 2013, 01:33 PM #2 Member   Joined: Oct 2012 Posts: 39 Thanks: 0 Re: Estimate the value of this sum... Would I find the integral? I did that and my answer was about 15 off, but a pretty close approximation.
 April 18th, 2013, 01:25 PM #3 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Estimate the value of this sum... [color=#000000]Here is a better approximation using $\int_{a}^{b}f(x)\;\mathbb{d}x\approx\frac{b-a}{N}\sum_{k=0}^{N-1}f(x_{k})\Leftrightarrow \sum_{k=0}^{N-1}f(x_{k})\approx\frac{N}{b-a}\int_{a}^{b}f(x)\;\mathbb{d}x$ and for a=1000, b=8000, $x_{n}=\sqrt[3]{n+1000}$, N=8000-999=7001 you get $\sum_{k=1000}^{8000}\sqrt[3]{k}\approx\frac{7001}{7000}\int_{1000}^{8000}\sqrt[3]{x}\;\mathbb{d}x=\frac{1575225}{14}\approx 112516$ Mathematica gives the result $\sum_{k=1000}^{8000}\sqrt[3]{k}\approx 112515$, so the error is around 1 (no too big I guess). .[/color]

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