Help finding Power Series

[random88hero]

Hello All,

Can someone help me because I feel like I am solving this correctly but I am not sure if I am doing something wrong.

I was given the function

f(x) = ln(1-6x) and told to find the power series

So, by the integration rules I can up with ...

((6x)^(n+1)) / (n+1)

I am being told this is incorrect but when I take the integral I get 1/(1-6x) which fits the power series definition that would make the integral sum (6x)^n
then, taking the integral I would get my answer from above.

Any help?

 

[Deleted member 4993]

Hello All,

Can someone help me because I feel like I am solving this correctly but I am not sure if I am doing something wrong.

I was given the function

f(x) = ln(1-6x) and told to find the power series

So, by the integration rules I can up with ...

((6x)^(n+1)) / (n+1)

I am being told this is incorrect but when I take the integral I get 1/(1-6x) which fits the power series definition that would make the integral sum (6x)^n
then, taking the integral I would get my answer from above.

Any help?

Find power series expansion of:

\(\displaystyle \frac{-6}{1-6x}\)

Then integrate that to find power series expansion of ln(1-6x)

 

[random88hero]

would that just be

-6 (6x^(n+1))/(n+1)

with that, it would not be alternating because the - is coming from the top term and not the 6x correct?

meaning, when say... 1/1+x, the resulting power series would be alternating because we would have to take 1/(1-(-x))

 

[galactus]

The power series for \(\displaystyle ln(1+x)\) is

\(\displaystyle ln(1+x)=\sum_{k=0}^{\infty}(-1)^{k}\frac{x^{k+1}}{k+1}\)

Sub in -6x for x