Question

Find the Values for X so that the series converges.

The series is from n=1 to Inf of 10/x^n

What I did was remove the 2 from the fraction so I got 10(1/x)^n. I took the abs(1/x)<1 because geometric series must be below 1 to converge.

And the answer i received was (-1,0)U(0,1)

However this answer is wrong. I am sure I did something wrong, but i just do not know what.

Answer 1

take a limit or the ratio (n+1)/n

Answer 2

\[\lim\frac{10x^{-n-1}}{10x^{-n}}\]
\[\lim\frac{x^{-n-1}}{x^{-n}}\]
\[\lim x^{-n+n+1}=|x|\]
\[|x|<1~:~-1<x<1\]

Answer 3

Hmm I'm not quite sure what that ratio thing is. We are currently in Geometric series in the book right now.