CK12 Calculus - Single Variable

1. Find the powerseriesrepresentation(MaclaurinSeries)of and approximate to 6
   decimalplaces.


2. Find the powerseriesrepresentation(MaclaurinSeries)of.

FrequentlyUsedMaclaurinSeries
SomefrequentlyusedMaclaurinSeriesare listedbelow

Calculationswith Series

BinomialSeries
We havelearnedthe BinomialTheoremfor positiveintegerexponents:

wherethe Binomialcoefficientsare denotedby

and for

AS a simpleBinomialfunction,takea= 1 andb= x. Then

Letrbe a real numberand f(x) = (1 +x)r. Isf(x) equalto a seriesin the form of (BE) exceptthat theremay
be an infiniteseries?The answeris yes.
Theorem(BinomialSeries)Letrbe a real numberand |x| < 1. Then