Question

find interval of convergence using ratio test, need help :) screenshot included

Answer 1

I found \[\frac{ a(n+1) }{ a(n) }\] to be \[\frac{ n(x-1) }{ -5(n+1) }\]

Answer 2

but now I need to find the absolute value of that function. would that just be \[\frac{ n \left| x \right|+ n }{ 5(n+1) }\] ?

Answer 3

You actually want to find the limit of the absolute value of the ratio, so you want to find |(x-1)/(-5) * (n)/(n+1)| < 1.
note that |n/(n+1)| -> 1
so we need |(x-1)/(-5)| < 1
then we need to check the boundaries. ie (x-1) = 5