Question

I have a series question. See below

Answer 1

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

Answer 2

I found the error formula, but I am not sure how to pick the value for c. No interval was provided, and I know it is a Maclaurin. I saw online that people used 0 (the center) as c, but I am not sure why

Answer 3

I hate error problems so much

Answer 4

Btw I have to use the Lagrange error test. This is right before all of the other tests, so I am not supposed to use them

Answer 5

@zepdrix @SolomonZelman

Answer 6

@TheSmartOne

Answer 7

@Nnesha

Answer 8

@Michele_Laino

Answer 9

@FibonacciChick666

Answer 10

I'm sorry, it is very late for me, since it is 2:30 a.m. (Italy time zone) and I have to go to sleep.

Answer 11

Alright. Thanks anyways

Answer 12

thanks!

Answer 13

I accidentally closed it

Answer 14

Can you still help me?

Answer 15

Above my head !!

Answer 16

Ok. Thanks anyways

Answer 17

If you know anyone that can, please direct them here

Answer 18

uhm, so personally, would take that you proved the series for e^x then it's just multiplication of taylor series I think

Answer 19

for the proof bit. as for the error, I'll need to look some stuff up first

Answer 20

http://www.mathopenref.com/calclagrange.html

I have to assue we are using c=0 because it is convenient for a solution.

Answer 21

so anyways, you probably proved e^x in class, so then you change x to a series and e^x into a series then you get your series. At least that is what it looks like to me.

Answer 22

no promises, but I hope this helps