I have two equations:

f(x)=sin(x/2) at c=0

f(x)=ln(2x) at c=2

I need to find the equation for the Taylor series formula for each of them. So for the first one, I worked out the Taylor polynomial to be x/2-x^3/48.... I know n=1 from that. But how do I write the rest of the formula? Since it's Maclaurin, I know the formula is [f^(n)(0)(x)^n]/n!, but what numbers do I plug in?

The second is ln(4)+((x-2)/2)-(((x-2)^2)/8)+(((x-2)^3)/24)... So n=0, and the other formula applies: [f^(n)(c)(x-c)^n]/n!, but I have the problem with the numbers again.. I need this to get the interval of convergence via the Ratio test.

I would appreciate your help