anonymous
  • anonymous
how to take the derivative of series? for example ((-1)^n+1)(x-2)^n)/n
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
but you are a higher level than zarkon haha.
anonymous
  • anonymous
hell no term by term
anonymous
  • anonymous
is (-1)^n+1(x-2)^n-1 right?

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

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