The limit series can be simplified to a succinct expression: (n+1)/2n. For example, taking the first two sets of parantheses, we get 3/4 times 8/9 or 2/3. This is also equal to (3+1)/(2*3) or 2/3. So, at any point in the series, (n+1)/2n gives the result of the last multiplied terms. Thus, we can take the limit of (n+1)/2n as n approaches infinity. The denominator and numinator both have a degree of 1, but since the denominator has a coefficient of 2, the solution is 1/2.