Homework Statement
Hello, this is not a problem but I want some clarification with the following paragraph (starting my linear algebra course!):
Let S be any nonempty set and F be any field*, and let F(S,F) denote the
set of all functions from S to F. Two functions f and g in F(S, F) are...
Hmmm but I thought when you took the derivative of
Ʃ(n=1 to infinity) ((-1)^n)(x^(2n-1))(2n)/((2^(2n))(((m+1)!)^2) you get
Ʃ(n=2 to infinity) ((-1)^n)(x^(2n-2))(2n)(2n-1)/((2^(2n))((n!)^2))
Then if you change the index to n=1 you get:
Ʃ(n=1 to infinity)...
Homework Statement
http://imgur.com/FJhgN
Give this power series J(x) (leftmost in the picture), find the first and second derivative.
Homework Equations
You take the derivative of a power series term by term.
The Attempt at a Solution
I don't understand how to get the J''(x) in the...
1. Prove that the MacLaurin series for cosx converges to cosx for all x.
Homework Equations
Ʃ(n=0 to infinity) ((-1)^n)(x^2n)/((2n)!) is the MacLaurin series for cosx
|Rn(x)|\leqM*(|x|^(n+1))/((n+1)!) if |f^(n+1)(x)|\leqM
lim(n->infinity)Rn=0 then a function is equal to its Taylor series...