Tobias Holck Colding continues MIT's 18.100B Real Analysis with the Bolzano-Weierstrass theorem, proving that every bounded sequence contains a convergent subsequence, and then derives the Cauchy convergence theorem as a near-immediate consequence. The lecture moves into infinite series, starting with the geometric series as the foundational example, and addresses the central question of convergence testing. Colding introduces the comparison test in its two standard forms, working through the logic on the board in the style typical of MIT's OCW recordings. At 83 minutes, this is a full lecture session building directly on prior material in the course, aimed at students already comfortable with sequence convergence and basic real analysis definitions.