MAT 21C Lecture Notes - Lecture 9: Binomial Series, Absolute Convergence
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MAT 21C Full Course Notes
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Announcements: ec1 due oct 11, hw3 due oct 12, midterm 1 oct 14, o ce hours: m 3-4 msb 3106 t 2-3 olson 261 w 1-2 olson 125. 10. 2 the binomial series and applications of taylor series. A power series about x = a is a series of the form. Theorem 18. (the convergence theorem for power series) if the power series. Xn=0 anxn = a0 + a1x + a2x2 + 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|. Let f be a function with derivatives of order k for k = 1, 2, . , n in some interval i containing: then for any integer n from 0 through n , the taylor polynomial of order n generated by f at x = a is the polynomial.
