series convergent or divergent by ratio test

Please determine whether the series is convergent or divergent by ratio test.

Series (2n-1)/2^(3n)

First I solved that lim a(n+1)/an =1, so the test fails, now I am rethinking it and if I do a more accurate division lim = 1/8, which makes the series convergent.

So please help to find the correct answer by ratio test.

Thank you

where is the mistake in the calculation below

Then, please explain where is the mistake in the calculation below

Lim [2(n+1)-1/2^(3(n+1))] / [(2n-1)/2^(3n)] = lim (2n+1) / 2^(3n) 2^3) times 2^(3n)/92n-1) = lim (2n+1)/(16n-8)= 1/8

I substituted 2^(3n+3) by 2^(3n) times 2^3