Today we made us of the new skill we learned yesterday, which was dealing with negative exponents. So for today’s class we tackled a fairly old problem; what is the sum of an infinite number of fractions, and we expressed the fractions as negative powers of 2.
For example:
2-2 + 2-3 + 2-4 + … 2-n = ?
What we found, if we converted the exponents into fractions, was that each addition of the next negative power of 2 brought us closer to 0.5. This was pretty interesting, but we needed further proof that an infinite number of negative exponents summed to a finite decimal. To prove this we pulled out scissors and decided to cut up our work. With some strategic cuts, we were able to show physically that by continually adding fractions, the sum was ½.
Below are two pictures of the final product of the lesson.
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