[CSC 335] Problem 3 in Section 1.3

[Andrew J. Pounds]

In class today I showed how to answer problem 3 using code -- but 
because the terms of the series are always decreasing you could have 
just as easily answered the question with some simple logic.

For example the terms of the sum to make π\pi are.

4x2i−12i−14 \frac{x^{2i-1}}{2i-1}

This term oscillates between negative and positive, but what we want to 
know is when does its value drop below 0.001.  Remember, in our scenario 
x=1 so the numerator will ALWAYS be 1.  The problem then reduces to what 
value of i reduces the term 4/(2i+1) to 0.001.  In this case i=2000.

If we do the second part, and look for when the term drops to less than 
1e-10, then i=20,000,000,000 (and that will take a long time to converge!)

-- 
*/Andrew J. Pounds, Ph.D./*
/Professor of Chemistry and Computer Science/
/Director of the Computational Science Program/
/Mercer University, Macon, GA 31207 (478) 301-5627/
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