Find taylor series for f centered at 4 if....

f^(n)(4)=((-1)^n)nfactorial/(3^n)(n+1)

what is the radius of convergence?

Question

Find taylor series for f centered at 4 if....

f^(n)(4)=((-1)^n)nfactorial/(3^n)(n+1)

what is the radius of convergence?

anonymous · Answer

Can you type it in the equation format. That is hard to read :/

anonymous · Answer

okay...never tried the equation but okay

anonymous · Answer

$$f ^{n}(4)=(-1)^{n} n!/3^{n}(n+1)$$

anonymous · Answer

Okay, the only question I have is...you have f^n(4) but there is no x to plug in the 4?

anonymous · Answer

ummmm I gess they replace that?

anonymous · Answer

sorry something happened to comp

anonymous · Answer

I have no idea how to solve that without it being a series with an x

anonymous · Answer

oooo hahaha good try then?

anonymous · Answer

Well, if you have an infinite series. You can use the ratio test which forces it to be less than 1 for convergence. From there you can solve for x. (the radius)

anonymous · Answer

oooo okay alright thank you! I'll figure it out from here