Tobias Holck Colding continues MIT's 18.100B Real Analysis course with a lecture spanning several core topics in sequence and series theory. He reviews limsup and liminf as tools for handling sequences that do not converge in the ordinary sense, then moves into power series, examining radius of convergence and term by term behavior. The central construction is the exponential function, defined directly as a power series rather than through calculus shortcuts, with Colding working through the early steps needed to prove its basic algebraic and continuity properties. The lecture closes by tying this back into a broader discussion of continuous functions, showing how the power series definition connects to the general theory built earlier in the course. Delivered as a standard chalkboard lecture running just under an hour and a half, it assumes familiarity with prior sessions on sequences and series.