Question

Need help with function represented by this series!

Answer 1

Recall that for \(|x|<1\),
\[\sum_{n=0}^\infty x^n=\frac{1}{1-x}\]

Answer 2

Yeah, i got that. I just can't figure out how to manipulate it to work for this particular problem.

Answer 3

Using that fact,
\[\sum_{n=0}^\infty (x+6)^n=\frac{1}{1-(x+6)}=\frac{1}{\cdots}\]

Answer 4

After I do that, I get 1/(-5-x).. so the answer would be B.) right?

Answer 5

Close, factoring out \(-1\) does the following to the denominator:
\[-5-x=-1(5+x)~~\implies~~\sum\cdots=-\frac{1}{x+5}\]

Answer 6

Ah, I see. Thanks so much!

Answer 7

yw