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Old 07-06-2008   #1
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Default Approximation / Leibniz

Can you help me solve this problem using Leibniz theorem?

How many terms are needed in the taylor expansion of cos x to computer cos x for |x|<0.5 accurate to 12 decimal places (rounded)? The answer in the book is "at least 7 terms". But I need hints. I started with x^(2[n+1])/(2[n+1])! < 10^-12, but I didn't know how to continue.