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

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

Mathematics
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but you are a higher level than zarkon haha.
hell no term by term
is (-1)^n+1(x-2)^n-1 right?

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yes i believe so , let me write it so i don't do anything silly are we starting at n = 0 or n = 1?
yes that is right. what you have
1. okay and then i got the interval of that to be 1
same
oh but not at the endpoints of course
next question...can you explain how to find the power series of a function?
i can show you a trick for that one if you like
well maybe not
yes please! i have an exam tomorrow and i need as much help as possible.
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
but if you have an exam forget that mess
and also your derivative will not convege at the endpoints, because there is not way that \[\sum 1^n\] or \[\sum (-1)^n\] converges
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) = \[\sqrt[4]{1+x}\]
i guess you are supposed to write this as \[(1+x)^{\frac{1}{4}}\] first and then use "general binomial series
er \[1+\frac{1}{4}x+\frac{\frac{1}{4}-1}{2!}x^2\]
\[+\frac{(\frac{1}{4}-1)(\frac{1}{4}-2)}{3!}x^3 +...\]
probably some algebra will turn up a nice pattern
but i dont understand the maclaurin part?
that is the maclaurin series
expand about zero, get \[a_0+a_1x+a_2x^2+a_3x^3 + ...\]
you can do this using the usual derivative method, but the generalized binomial formula will work in this case
wait what about the thing where you take the derivative multiple times and plug it in?
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
the hint was "binomial" formula
ohh oops. i am terrible at math! and context clues i guess haha. well, do you have any test-taking tips ?
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
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
good luck
that first part of the tip is so true! anyway thank you so much. you are a lifesaver. seriously.
your quite welcome, and really good luck and relax and don't stay up all night studying

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