I want to know that in a closed traverse the sum of latitude and departure is always zero,why?

In a closed traverse you end up exactly where you started. So if you started at (0,0) you will end up at (0,0), this applies to the traverse AFTER it is adjusted. You will never end up at your beginning coordinates when you use your raw (unadjusted) angles and distances. The difference between where you started and where you ended will give an idea of the accuracy of your field work.