# lecture12_Sarka_Fa19.pdf - Math 231 Lecture 12 • Quiz 2...

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Math 231 Lecture 12 10/7/19 Quiz 2 in discussion sections tomorrow! Arclength, Surf. Area, Hydrostatic Force, Moments, Sequences & Series HW 11 (Series, Integral Test) due Friday 8:30am Final Exam for Math 231 on Monday, 12/16/2019, from 7PM to 10PM. 11.2 Series X n =1 a n = a 1 + a 2 + a 3 + a 4 + . . . Def: Sequence of partial sums Def: X n =1 a n converges if Test for Divergence: If lim n →∞ a n 6 = 0, then X n =1 a n diverges. Ex: X n =1 n 2 + 1 2 n 2 - 3 1
Geometric series X n =0 r n = 1 + r + r 2 + r 3 + . . . Recall: lim n →∞ r n = 0 if | r | < 1 1 if r = 1 otherwise X n =0 r n = if | r | < 1 if | r | ≥ 1 Does X n =0 r n with | r | < 1 converge or diverge? a + ar + ar 2 + . . . = a (1 + r + r 2 + . . . ) = a X n =0 r n Ex: 20 3 + 40 9 +

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