Coconut Problem - Challenging

The Ultimate Puzzle Site - Brain-Teasers

Same question as there, but this problem only deals with 3 sailors and instead of splitting 1/5, they split 1/3 each time. Does this method work? If so, can someone help me complete it; I don't like their way of solving it.

Let n = total # of coconuts. Then,

(n - 1) - 1/3(n - 1) is after the 1st sailor;

Then, let k = (n - 1) - 1/3(n - 1), and after the 2nd sailor will be:

(k - 1) - 1/3(k - 1)

Then, let m = (k - 1) - 1/3(k - 1), and after the 3rd sailor will be:

(m - 1) - 1/3(m - 1);

Finally, when they all wake up and give 1 away and then split the remaining, we have to do it one more time.

Let n = (m - 1) - 1/3(m - 1), and thus the final answer is:

(n - 1) - 1/3(n - 1)...

Ok, now the tricky part is substituting that in. I have a whole white board filled up with substitutions, and it gets extremely messy with parentheses etc. Can anyone help?