MAT 21C Lecture Notes - Lecture 3: Convergent Series, Integral Test For Convergence, Rational Number
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MAT 21C Full Course Notes
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Announcements: hw1 due w sept 28, discussions forum. The following six sequences converge to the limits listed below: ln n. 1. n 0: n n = 1, c1/n 1 (c > 0, cn 0 (|c| < 1) n(cid:17)n, (cid:16)1 + Theorem 6. (the monotonic sequence theorem) if a sequence {an} is both bounded and monotonic, then the sequence converges. Given a sequence of numbers {an}, an expression of the form. Xn=1 an = a1 + a2 + a3 + + an + k=1 ak is the nth partial sum. is an in nite series. The sequence {sn} is the sequence of partial sums of the series. Theorem 7. an converges, then an 0. Xn=1 an diverges if lim n an fails to exist or is di erent from zero. Xn=1 bn = b are convergent series, then: sum rule: x(an + bn) =x an +x bn = a + b.
