Question

how to take the derivative of series? for example ((-1)^n+1)(x-2)^n)/n

Answer 1

but you are a higher level than zarkon haha.

Answer 2

hell no
term by term

Answer 3

is (-1)^n+1(x-2)^n-1 right?

Answer 4

yes i believe so , let me write it so i don't do anything silly
are we starting at n = 0 or n = 1?

Answer 5

yes that is right. what you have

Answer 6

1. okay and then i got the interval of that to be 1<x<3, but i am having trouble with the convergence of course.

Answer 7

same

Answer 8

oh but not at the endpoints of course

Answer 9

next question...can you explain how to find the power series of a function?

Answer 10

i can show you a trick for that one if you like

Answer 11

well maybe not

Answer 12

yes please! i have an exam tomorrow and i need as much help as possible.

Answer 13

well then i don't want to waste your time with this. but if you know that
\[\frac{1}{1-x}=\sum x^n\] then
\[\frac{1}{1+x}=\sum (-1)^nx^n\] and so
\[\frac{1}{x-1}=\frac{1}{1+(x-2)}=\sum(-1)^n(x-2)^n\] so that is your derivative, and therefore your original series was the log

Answer 14

but if you have an exam forget that mess

Answer 15

and also your derivative will not convege at the endpoints, because there is not way that
\[\sum 1^n\] or
\[\sum (-1)^n\] converges

Answer 16

this is not wasting my time at alll. umm soo what about htis: use the binomial series to find the maclaurin series of the function f(x) = \[\sqrt[4]{1+x}\]

Answer 17

i guess you are supposed to write this as
\[(1+x)^{\frac{1}{4}}\] first and then use "general binomial series

Answer 18

er
\[1+\frac{1}{4}x+\frac{\frac{1}{4}-1}{2!}x^2\]

Answer 19

\[+\frac{(\frac{1}{4}-1)(\frac{1}{4}-2)}{3!}x^3 +...\]

Answer 20

probably some algebra will turn up a nice pattern

Answer 21

but i dont understand the maclaurin part?

Answer 22

that is the maclaurin series

Answer 23

expand about zero, get
\[a_0+a_1x+a_2x^2+a_3x^3 + ...\]

Answer 24

you can do this using the usual derivative method, but the generalized binomial formula will work in this case

Answer 25

wait what about the thing where you take the derivative multiple times and plug it in?

Answer 26

yes you can do that, but it is a pain. problem said "binomial" so i used it.
take a look here
http://www.proofwiki.org/wiki/Binomial_Theorem/General_Binomial_Theorem

Answer 27

the hint was "binomial" formula

Answer 28

ohh oops. i am terrible at math! and context clues i guess haha.

well, do you have any test-taking tips ?

Answer 29

get some sleep and don't study right before the test, it will only freak you out when you see what you don't know
ok easier said than done, i know
relax though, it helps

Answer 30

but i do not believe you are terrible at math because this is fairly advanced stuff, and in any case you found the intervals of convergence yourself
also look at assigned homework problmes, and especialy quizzes because professors tend to repeat themselves, or at least ask the same types of questions

Answer 31

good luck

Answer 32

that first part of the tip is so true! anyway thank you so much. you are a lifesaver. seriously.

Answer 33

your quite welcome, and really good luck and relax
and don't stay up all night studying