I have a series question. See below

Question

anonymous · Answer

I am supposed to prove that xe^x converges to $$\sum_{n=0}^{\infty}\frac{ x^{n+1} }{ n! }$$

anonymous · Answer

I got the error formula, except for the fact that no interval was provided, so I don't know how to choose c. Someone online I saw used 0 as c, but I don't know why. Btw, its a Maclaurin

solomonzelman · Answer

$\large\color{black}{ \displaystyle \sum_{ n=0 }^{ \infty } \frac{x^n}{n!}=e^x}$

anonymous · Answer

Yes

anonymous · Answer

Then I multiplied it by x

solomonzelman · Answer

yes

anonymous · Answer

And I found the error formula, except for evaluating the nth derivative at c

anonymous · Answer

And I have no idea how to choose c. The people online used 0 (the center) as c, but I don't know why

anonymous · Answer

And that is my question

solomonzelman · Answer

I am not very aware, or don't remember the error formula, can you cite it please ?

anonymous · Answer

Yes

anonymous · Answer

@SolomonZelman, After you are done with this person. Can you please help me?

solomonzelman · Answer

perhaps

anonymous · Answer

Rn(x)$$\le \frac{ f ^{n+1}x ^{n+1} }{ (n+1)! }$$

anonymous · Answer

$$f ^{n+1}(c)$$

anonymous · Answer

Sorry, I messed up that part of the formula

solomonzelman · Answer

don't really know that right now.... will say I am not good at it, sorry.
gtg

anonymous · Answer

Ok... thanks anyways