In order to decide on convergence or divergence of the above two improper integrals, we need to consider the cases: p<1, p=1 and p >1. Helpful? In this section we will discuss in greater detail the convergence and divergence of infinite series. Share. A divergent sequence doesn’t have a limit. University. Here’s an example of a convergent sequence: This sequence approaches 0, so: Thus, this sequence converges to 0. Moreover, we have is convergent if and only if p <1 is convergent if and only if p >1 So, the difference between convergent integrals and divergent integrals is that convergent integrals, when evaluated, go to a specific value whereas a divergent integral, when evaluated does not go to a finite value and goes to ± ∞. We will illustrate how partial sums are used to determine if an infinite series converges or diverges. We will also give the Divergence Test for series in this section. Please sign in or register to post comments. A convergent sequence has a limit — that is, it approaches a real number. Related documents. Calculus (MAT00001C) Academic year. 0 0. University of York. Lecture notes on the differences between convergent and divergent series. Comments. If p <1, then we have and If p=1, then we have and If p > 1, we have and The p-Test: Regardless of the value of the number p, the improper integral is always divergent. 2017/2018. Calculus notes 09 Gamma function Calculus- Second order differential equations notes Calculus … Here’s another convergent sequence: This time, the sequence […] Convergent vs Divergergent explanation. These of course represent areas.


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