Integral Test—Harmonic Series, p-Series
Lecture no. 19 from the course: Understanding Calculus II: Problems, Solutions, and Tips
Taught by Professor Bruce H. Edwards | 30 min | Categories: The Great Courses Plus Online Mathematics Courses
Does the celebrated harmonic series diverge or converge? Discover a proof using the integral test. Then generalize to define an entire class of series called p-series, and prove a theorem showing when they converge. Close with the sum of the harmonic series, the fascinating Euler-Mascheroni constant, which is not known to be rational or irrational.