May 12th, 2010, 04:02 PM  #1 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  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. 
May 12th, 2010, 08:35 PM  #2 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  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?

May 13th, 2010, 05:17 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
The question is poorly worded, but I think it means a Taylor series something like f(a + h) = f(a) + hf'(a) + (h²/2!)f''(a) + ... + remainder term, subject to certain conditions, where f is cos, a is xo, and x = a + h. The righthand 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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convergence, series, taylor 
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