My papa sparked a desire to understand wacky series, when he told a 9-year-old me that the alternating harmonic series can sum to whatever you wish it to. Addition commutes, except if you do it lots and lots?!
A happy two hours exploring this with FM class, using Excel without fully trusting Excel.
Best Student Quotes:
- “If the alternating harmonic series can converge to anything, does that mean 1 – 1 + 1 – 1 … also can?”
- “1 + 1/4 + 1/9 + 1/16 + … is an infinite sequence of squares. Lined up they are infinitely long, but do they have an infinite area? Oo, isn’t that like Vsauce?”
- “Eventually the percentage of numbers with a 9 in them is basically 100”
- “I jump to the right more and more, and then end up … on the left?!” yells W as she hops around the room angrily (-1/12).
- “Don’t worry sir, it doesn’t take too long to add up the first 50,000 terms”
- “I feel dumb in Further Maths”. Obvious Warning: if it is too hard, people will drop out. How to ensure students know that this kind of thing is not on the exam, without constantly referencing exams?