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For any given real number, its corresponding continued fraction is unique. However, given an arbitrary continued fraction, there has been no general way to identify its corresponding real number. In this paper we shall show a general algorithm from continued fractions to real numbers via infinite sums representations. Using this algorithm, we obtain some new Tasoev continued fractions.doi:10.1090/s0025-5718-05-01752-7 fatcat:hwad5vczezgwjiltircvcyxcii