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May 12th, 2010, 04:02 PM   #1
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Convergence of Taylor Series

Prove the taylor series for cos x about any value x = xo converges to cos x for all x.

I just need help finding the series to start off. I can take it from there if anyone can help me find the series.Thanks.
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May 12th, 2010, 08:35 PM   #2
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Re: Convergence of Taylor Series

Would I just have to pick some arbitrary point and find the series using that point for xo, then just substitute that value and put xo after I find the series?
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May 13th, 2010, 05:17 AM   #3
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The question is poorly worded, but I think it means a Taylor series something like
f(a + h) = f(a) + hf'(a) + (h/2!)f''(a) + ... + remainder term, subject to certain conditions,
where f is cos, a is xo, and x = a + h. The right-hand side has n terms and a remainder term that depends on n.
Specify a suitable remainder term and show that it tends to zero as n tends to infinity (for any value of x).
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