Understanding 了: difference between 她上个月去了北京 and 上个月我去台湾了?
了 indicates 'completion of an action'

In "上个月我去了台湾" the action of "去" is completed, meaning you had gone there but it doesn't say you are still there or have already came back 

In "上个月我去台湾了",  '了' is a final particle for the emphasis (stress in tone) of the whole sentence 

You can see the different by compare the two structure with other context:


"下个月我去了台湾" is nonsensical, you can't already gone there when you say 'next month'
'了' in "下个月我去台湾了"  is a final particle for emphasis, and this sentence does make sense