Recent content by stupidmonkey

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...