A curious sequence
This nifty investigation ties together your work on sequences with decimal-fraction equivalence and Pythagorean triples. It also introduces the idea of limits.
Starting with a sequence of fractions, students need to
- identify how to create each term from the previous
- use a calculator to convert to decimals and discover the limit of the sequence is √2
- split the numerators of the fractions into two consecutive numbers, forming Pythagorean triples within each odd term
- discover the result of changing the first term.
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