Решение:
- I have been dieting (to diet) for the past few years. I have tried (to try) all sorts of diets.
- I've been doing (to do) a lot of sports during the last month. I've been playing (to play) three types of games.
- I've been studying (to study) a lot for the last week. I've been writing (to write) two essays.
- I've been traveling (to travel) a lot for the last two years. I've been visiting (to visit) four countries.
- My friend's has been smoking (to smoke) for two years. He's got problems with his health.
- I have been taking (to take) dancing lessons for a month. I have been learning (to learn) three dances.
Ответ: 1. been dieting, tried; 2. been doing, been playing; 3. been studying, been writing; 4. been traveling, been visiting; 5. has been smoking, got; 6. been taking, been learning.