Question

Need to learn how to do power series: y=(e^x-1)/x, use taylor series for e^x and substitution

Answer 1

\[y=e^{x}-1/x\]

Answer 2

Taylor series for e^x is just 1 for f', f'',f'''

Answer 3

y= e^x - 1/x

Answer 4

ended up with \[1+x+x^{2}/2!+x ^{3}/3!\], geometric I think, but how do we get to that answer?

Answer 5

not geometric but yes, that's correct. :D good job.

Answer 6

geometric would be without the factorial I see.

Answer 7

remember geometric is \[\huge \sum a_nr^n\]

Answer 8

Right, but how do we figure these out. i got lost when i got to this section...
Kind of need a step by step I guess

Answer 9

series are tricky. Honestly, exposure is the only way to know what is what. You'll often see geometric series where the whole thing is raised to a power of n, and the inside is just some finite value.

Answer 10

So would this be a case where it is divided by n! ?

Answer 11

yup it would.

Answer 12

\[\sum_{0}^{\infty}x ^{n}/n!\]

Answer 13

?

Answer 14

for all x >0 because if x=0, then you have problems.

Answer 15

Nice. I didn't realize I had it that close last night. Thanks.

Answer 16

check out my calc sheet i made a year ago. There are a few typo's on it but the power series stuff is correct. https://docs.google.com/open?id=0B98cXMBCs13BYzRhNDBkMGYtMjc2YS00MWZiLTlmOGMtNDM1ODIxNjU0YTMw

Answer 17

in your case, heart = x. :D My teacher had a sense of humor when going over series. hahaha.

Answer 18

Wow!

Answer 19

don't rely on it too heavily. Some of the convergence test stuff is worded a bit incorrectly. I think the derivative of arctan is not under a sqrt either.

Answer 20

http://openstudy.com/updates/500cd99be4b0549a89329266 is my trig sheet too. that one is more solid.

Answer 21

I have another one if you wouldn't mind. but it does have to do with the derivative of arctan...

Answer 22

close this one and ask away :D I'll keep my eye out for it. :D

Answer 23

Thanks