Convergent and uniformly convergent sequences of functions. A uniformly convergent sequence of continuous functions converges to a continuous function. Partial sums of a sequence of functions with values in \(\mathbb {C}\) , series of functions. Convergence, uniform convergence and absolute convergence of a series of functions. A series of functions absolutely convergent is convergent. Weierstrass criterion for the uniform convergence of a series of functions. Upper and lower limits of a real numerical sequence. Power series. The geometric series. Radius of convergence, Abel’s theorem. Ratio criterion.