The usual argument to compute the sum of the binomial series goes as follows.
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The binomial series is therefore sometimes referred to as Newton's binomial theorem.
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Taking r =-1, the generalized binomial series gives the geometric series formula, valid for | x |:
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Variations of this argument can be used to produce continued fraction expansions for the natural logarithm, the generalized binomial series.
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It can be evaluated by expanding the integral by the binomial series and integrating term by term : see Meridian arc for details.
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And then the bit in that section that says " For a more extensive account of Newton's generalized binomial theorem, see binomial series "?
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Taking the reciprocal of this gives \ frac { 1 } { 1-q }, which can be expanded as a binomial series in q.
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The first results concerning binomial series for other than positive-integer exponents were given by Sir Isaac Newton in the study of areas enclosed under certain curves.
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