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: 20,616 Thanks: 2072 
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). 

Tags 
convergence, series, taylor 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Convergence test using taylor series  bereprada  Complex Analysis  0  March 11th, 2014 05:34 PM 
In need of help disk, series test, taylor, and power series  g0bearmon  Real Analysis  2  May 22nd, 2012 12:10 PM 
how to find the interval of convergence of Taylor's series?  dkssudgktpdy  Real Analysis  2  April 5th, 2011 10:14 PM 
Taylor Series  stewpert  Calculus  3  February 10th, 2010 01:15 PM 
In need of help disk, series test, taylor, and power series  g0bearmon  Calculus  1  December 31st, 1969 04:00 PM 