Hi Everyone! Today we are asked to find a Taylor Series for at about its center, a=4. I've been working on this one problem for hours now, and I feel so dumb not being able to find a Taylor series for it. So far I've been working on formulas. So far, the nth derivatives goes like this: . The easy part is that the denominator is a base 2 power function and can be given by . The alternating signs can be given by . But the numerator is the real problem. It can be given by 1,1,1*3,1*3*5,1*3*5*7... which is somewhat equal to simply . But the problem is, instead of the numerator going: 1,3 ,15,105... it instead goes: 1,1,3,15,105...

That first numerator is giving me problems. Anyone got any ideas on how I should proceed with this or at least, how to give find the Taylor series for this function? Thanks everyone in advance.