Anyone here good with Taylor series? :)

[fiji885]

Any help would be appreciated. This is Summer, and I am dying. Figuratively, of course. My answer is a little off to the one that is the supposedly correct answer. I don't see how they can get still have (n+1) in their final answer. Anyone know where I went wrong?

https://i.imgur.com/WE8nrms.png

[lastchance]

Are you expanding about x=1 or x=2? (Or am I misreading your squiggle?)

https://imgur.com/a/NvHrZkI

Fundamentally, you get a (n+1) in the final answer because you divide factorial(n+1) by factorial (n), from which (n+1) is the only uncancelled factor.

[fiji885]

Thank you so much, lastchance. I had my f^(n)(x) equation incorrect.