MAT 21C Lecture Notes - Lecture 6: Ibm System P, Alternating Series, Asteroid Family
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MAT 21C Full Course Notes
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Announcements: hw2 due oct 5, ec1 due oct 11, hw3 due oct 12, hw3, midterm1 oct 14. Recap: sequences {an, series p an, sequence of partial sums of series {sn, common series: Geometric series: |r| < 1 conv, |r| 1 div. P-series: p > 1 conv, p 1 div: tests for series convergence/divergence (caution: will not help obtain the sum of series!) The nth-term test for divergence: an 6 0 series diverge. The integral test: if f cont,pos,dec and r f conv series conv. The comparison test: an cn and p cn conv p an conv dn an and p dn div p an div. The limit comparison test: for an > 0, bn > 0 an bn an bn an bn. C > 0 both conv or both div. 0 and p bn conv p an conv. And p bn div p an div. The absolute convergence test: if p |an| conv then p an.
