Recent content by knotman2

= (x-2)^2\left(\sum_{k=2}^\infty (x-2)^k\right)' = (x-2)^2\((1/1-(x-2))-1-(x-2))' = (x-2)^2\((1/(x+1)^2)-1) ?

okay so (x-2)^2\(sum_{k=2}^\infty k(x-2)^{k-1})' (x-2)^2\(sum_{k=2}^\infty (x-2)^{k}) (x-2)^2 (1/1-(x-2))' =(x-2)^2 (1/(x+1)^2?

(x-2)^2 sum of from k=2 to infinity of k(x-2)^k-1

k(x-2)^2(x-2)^k-1

Also how do i deal with the k(k+1)?

I tried doing k(K+1)(x-2)^2(x-2)^k-2… this doesn't really look like the derivative of anything?

have added now to the question above.

Homework Statement Determine the radius of convergence, the interval of convergence, and the sum of the series Summation from k=2 to ∞ of k(x-2)^k+1. Homework Equations ratio test? The Attempt at a Solution possibly take the derrivitive of the power series, then find the sum then integrate...

How does [cos(x),-sin(x)] = span[sin(x),cos(x)]? and also… i think it is a bit quick to say that because of this statement any f can be written from a linear combination of y..is y the function?