Reference: http://www.binbaz.org.sa/mat/17194
Question: A questioner is saying that she fasted the first days of Dhul-Hijjah?
Response: There is no problem if she fasts the seventh, eighth or ninth (of Dhul-Hijjah), there is no problem in this, or if she fasts more than this.
The point is that they are days; days of Dhikr and fasting, if she fasted all nine days then this is good, if she fasts a part of the ten, then this is also good, it is all good.
If she suffices with fasting only ‘Arafah, then this is the best day, indeed the Prophet – صلى الله عليه وسلم – said:
"I anticipate that the day of ‘Arafah expiates the sins of the year before it and the year after it.". It is a tremendous day, everybody should fast it except the pilgrims who are not to fast on the day of ‘Arafah.
Likewise are the rest of the days, from the first day of Dhul-Hijjah to the day of ‘Arafah, it is recommended to fast the nine, but the best day is the day of ‘Arafah. It is recommended to fast it whether you live in Makkah or the country side.
The exception is the day of ‘Eed, it is not to be fasted by the pilgrim or others. It is the Sunnah for the pilgrim not to fast on the day of ‘Arafah, rather he/she should eat as the Prophet – صلى الله عليه وسلم – was not fasting on the day of ‘Arafah.