Math Easy Solutions (@matheasysolutions)

In this video, I use the Integral Test to show that the p-series, whose terms are 1/n^p, is convergent if p is greater than 1 and divergent for all other values of p. When p is less than 0, the terms approach infinity; when p = 0, the terms equal 1, hence it is divergent by the test for divergence; and when p = 1, we get the harmonic series, which is also divergent. I also illustrate this with examples on a convergent and a divergent p-series. Note also that when using the Integral Test, the corresponding improper integrals do NOT, in general, equal the sum of the series. https://3speak.tv/watch?v=mes/the-p-series--1np-is-conver-363 & https://youtu.be/64ltC272FSQ #math #calculus #series #pseries #education