series convergent or divergent by ratio test
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.
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