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Transforming numbers
Member rating: No Rating | Words: | Submitted: Wed Aug 13 2003
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TRANSFORMING NUMBERS Name: Waseem Ahmed Course: PGCE Mathematics Question a › a + 2b where a,b are whole numbers b a + b 1 › 3 › 7 › 17 ›....... 1 2 5 12 Investigate transformations of this kind Problem Statement This problem involves fractions and the aim is to investigate how these numbers can be transformed to the next number in the sequence. How will I go about investigating this problem? First I will like to know where this sequence leads me. From this I will get a better idea of approaching the problem. Approach Using excel spreadsheet, starting with numerator and denominator being equal, ie a=1 and b=1. I found that the sequence of the transformation eventually converging to the square root of 2. a equal to b (a=b=1) Sequence Sequence Table 1 of of a=b=1 Numerator Denominator Result 1 1 1 3 2 1.5 7 5 1.4 17 12 1.4166667 41 29 1.41337931 99 70 1.4142857 239 169 1.4142012 577 408 1.4142132 1393 985 1.4142136 3363 2378 1.4142136 From table 1, it was noticed that the sequence converges towards V2. I...
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