MATH 1XX3 Lecture 21: Lecture 21
2 Mar 2016
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Goal : define a function with an infinite. = cot c , xt gx2 + c}x3 + (cid:572) power series. More generally , a series of the form (cid:572) power series centered at 2 know. , gc - a ) + gcx . apt . series are functions. Note : power centered at a is defined ) (ie + 4 ( x - 213 + , sh we wantto x will make this is always defined at the value thedomain (where. = co to + ot . series converge is centered at power series. , ( a -a) a we get : we plug a co t c it. + y + if + (applythe ratio test ) m%mhi tt yt o a) The ratio lest implies that ftod willconverge for all x. Power series only converges at: - a. There is a number r such that the series converges if. / x. a k r and diverges if.
