MAT 21C Lecture Notes - Lecture 4: Ibm System P, Integral Test For Convergence
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A*r n-1 converges to a/(1-r) if |r| < 1. This test states that if a series doesn"t approach 0, then it diverges. **note that this does not imply that if a n does approach 0, it always converges ** A harmonic series is simply a p-series with p = 1. E. g. : 1 + + + + + 2-series: 1 + + 1/9 + 1/16 + . 3-series: 1 + + 1/27 + 1/64 + . There is a simple formula for determining convergence and divergence of p-series, and it was derived using the integral test. Know: ** p-series converge if p > 1 and diverge if p <= 1 ** The integral test is used to prove harmonic and p-series behaviors. Assuming all terms of a n are positive and there"s a function f with f(n) = a n and f is a decreasing function.
