Question

Starting with the known power series representation
1/(1−x) = ∑ (from n=0 to ∞ of )x^n, |x|<1,

determine the power series representation for the function
6/6−x

in powers of x. Also find the interval where the representation valid.

Answer 1

\[\frac{ 1 }{ 1-x }=\frac{ 6 }{ 6 }*\frac{ 1 }{ 1-x }=\frac{ 6 }{ 6-(6x) }\] As x->0, 6x->0
You could put X=6x

Answer 2

I think I've managed to get to this:

\[\sum_{n=0}^{\inf} (x/6)^n\] Now im thinking of taking
R = 1 / \[\lim_{n \rightarrow \inf}\left| \frac{ a1 }{ a2 } \right|\]

Answer 3

\[\sum_{n=0}^{\infty} (x/6)^{n} when |x|<\frac{ 1 }{ 6 }\]

Answer 4

Sorry made a little mistake there. \[\sum_{n=0}^{\infty}(x/6) ^{n} when |x|<6\]