Shavua Tov. We end our holiday season with הושענא רבא, שמיני עצרת, and שמחת תורה. The seventh day of Succot is הושענא רבה. It is the final day to ask for forgiveness and achieve atonement. In the Beit Hamikdash, the custom was to circle the מזבח seven times with Lulav and Etrog. This was followed by the taking of the willow and beating it several times.
The willow was the one specie that had no smell and no taste. It symbolized the sin. Therefore, it is the one that is smashed.
In Israel, we combine שמיני עצרת and שמחת תורה into one day. At night and in the morning, we do הקפות and celebrate completing the Torah. We also say Yizkor and the prayer for rain, תפילת גשם. This last holiday of שמיני עצרת is a חג בפני עצמו, a separate holiday. Hashem did not want to part with His children and asked them to stay another day. This is why we say שהחיינו on שמיני עצרת. Chag Sameach!