What is the source for starting a new limmud (learning) immediately after finishing the previous one? For example After finishing one mesechta I have seen people immediately start the next one, even if it means only reading the first few words.
Perhaps the practice parallels the practice in some communities of reading the beginning of Bereishit just after finishing the Torah on Simchat Torah. The Tur wites about this (OC 669):
ורגילין להתחיל מיד בראשית כדי שלא יהא פתחון פה לשטן לקטרג לומר כבר סיימו אותה ואינם רוצים לקרותה עוד
And we are accustomed to start immediately [reading the portion of] Bereishit so that the accusing angel cannot open his mouth to accuse and arraign saying: they have finished it and don't want to read it anymore.
By beginning to learn another book you symbolize that you have not finished in the absolute sense as there is always more to learn.
Psalm 84:7. "They go from strength to strength.."
Ok, I still think this verse is the real source so I am expanding the answer:
at the final page of meseches berachos the talmud says: Reb Chia the son of Ashi said in the name of Rav, Talmidei Chachomim don’t have tranquility in this world and not in the next world (they go from one yeshivah to the next) as it says; They will go from strength to strength, they will be seen by G-d in Tzion.
I think this gemora is the reason why we start another tractate. the fact that it is brought at the end of the first tractate seems to also support this.