Find the Taylor Series for f(x) centered at a=25. (assume f has a power series expansion)
I'm not going to type all these derivatives, but here are the 4th and nth:
So, when I calculated my nth derivative, I got:
No idea....
EDIT: Do I need to use the binomial series here?
Thanks! I am really struggling with this entire concept. Where did this come from? And where did this come from?
Sorry, I have been trying to understand this stuff for over a week and I can not get it...I desperately need someone to show it to me like I'm a 5 year old. Thanks so much for any help!
Try to spot the pattern:
Thus, the nth derivative should take on the form:
Now, the taylor series should be
I plugged this into Maple, and it gave me this simplification (which really isn't much...)
But I see NonCommAlg beat me to this...and his way looks much, much neater...