power series representation for 1/(1-x)^3, int. of converg.

[mymath]

find a power series representation for 1/(1-x)[sup:3fi1cv3k]3[/sup:3fi1cv3k] and determine the interval of convergence.
please help me to answer my last item on my exam

 

[pka]

Re: power series

find a power series representation for 1/(1-x)[sup:1p0zx26s]3[/sup:1p0zx26s] and determine the interval of convergence. please help me to answer my last item on my exam

Are you serious? You say that this is an exam and you are asking help with answering questions on the exam.

Well here is a hint.
\(\displaystyle \frac{1}{{1 - x}} = \sum\limits_{k = 0}^\infty {x^k } ,\quad \left|x\right|< 1\)
Can you differentiate?

 

[mymath]

actually, it was my previous exam...just trying to review my old exams

i got this solution, but i don't know if i got it right

Use the binomial series.



The binomial series is the form

=

Let u = -x and m = -3

The general form is

 

[Deleted member 4993]

If you differentiate (w.r.t x) the equation given by pka - twice - what do you get (on the left-hand-side and RHS - separately)!