MAT 21C Lecture Notes - Lecture 7: Absolute Convergence, Ratio Test, Commutator Subgroup
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MAT 21C Full Course Notes
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Announcements: o ce hours w1-3pm 2142 academic surge, hw2 due, hw3 due oct 12, ec1 due oct 11, hw3+, midterm 1 oct 14. A power series about x = c is a series of the form an(x c)n = a0 + a1(x c) + a2(x c)2 + + an(x c)n + . Xn=0 in which the center c and the coe cients a0, a1, are constants. Theorem 18. (the convergence theorem for power series) if the power series anxn = a0 + a1x + a2x2 + . Xn=0 converges at x = c 6= 0, then it converges absolutely for all x wtih |x| < |c|. If the series diverges at x = d, then it diverges for all x with |x| > |d|. Here r is called the radius of convergence. The interval of radius r centered at x = c is called the interval of convergence.
