For the source text click/tap here: Sukkah 46
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We have already established that outside of the Temple, on a biblical level the mitzvah of lulav is only on the first day of the holiday; our tradition of taking the lulav and etrog for the entire seven days of Sukkot is zecher le-Mikdash – a commemoration of the Temple where it was a mitzvah to take the lulav every day of the holiday (see Sukkah 41).
This is summed up in our Gemara, where Rabbi Yehoshua ben Levi declares that only the first day is the mitzvat lulav (the commandment of lulav); the rest of the week is mitzvat zekenim (the commandment of the Sages).
“Rav Yehuda said in the name of Shmuel: lulav, seven; and sukkah, one” (Sukkah 45b). So begins a discussion as to how often we are to make a bracha on these mitzvoth. Shmuel, the Gemara explains, is of the view that since there is one continuous mitzvah to sit in a sukkah for seven days and nights, “all seven are like one long day”; and hence, a bracha is recited only once. However, the mitzvah of lulav is applicable only by day, and not at night; and thus, each new day requires a new bracha.