From the Torah, the mitzvah of lulav is on the first day of Succos, but the mitzvah to be happy on Succos is for all seven days. The Imrei Noam zt’l says that this is to tell us that Hashem loves it when His nation is happy and in good spirits, therefore he made this mitzvah for seven days.

How much effort Bnei Yisrael invests to get the four minim! Some spend hours, seeking the best they can find. Let this be a sign of how much effort we should invest to be happy, for this is a mitzvah from the Torah for all seven days of Succos. ~ R’ Elimelech Biderman