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