Transcription of Power series and Taylor series - University of Pennsylvania
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Power series and Taylor series - University of Pennsylvania
Power series and Taylor seriesD. DeTurckUniversity of PennsylvaniaMarch 29, 2018D. DeTurckMath 104 002 2018A: Series1 / 42 SeriesFirst .. a review of what we have done so far:1We examined series of constants and learned that we can sayeverything there is to say about geometric and developed tests for convergence of series of considered Power series , derived formulas and other tricksfor finding them, and know them for a few DeTurckMath 104 002 2018A: Series2 / 421. geometric and telescoping seriesThe geometric series is n=0anrn=a+ar+ar2+ar3+ =a1 rprovided|r|<1 (when|r| 1 the series diverges).We often use partial fractions to detect telescoping series , forwhich we can calculate explicitly thepartial sums DeTurckMath 104 002 2018A: Series3 / 422.
1. Geometric and telescoping series The geometric series is X1 n=0 a nr n = a + ar + ar2 + ar3 + = a 1 r provided jrj<1 (when jrj 1 the series diverges). We often use partial fractions to detect telescoping series, for which we can calculate explicitly the partial sums S n. D. DeTurck Math 104 002 2018A: Series 3/42
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