Melting Brains with Infinite Series

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.




The students’ emotions at the end – thoroughly angry at Maths. Mission Accomplished

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?

Further links:




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