My Math Forum Convergence of Taylor Series

 Calculus Calculus Math Forum

 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 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).

 Tags convergence, series, taylor

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post bereprada Complex Analysis 0 March 11th, 2014 05:34 PM g0bearmon Real Analysis 2 May 22nd, 2012 12:10 PM dkssudgktpdy Real Analysis 2 April 5th, 2011 10:14 PM stewpert Calculus 3 February 10th, 2010 01:15 PM g0bearmon Calculus 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top