I'm usually a big fan of Numberphile but their most recent video seems to me to, at best, miss the point, and at worst, trade on dishonesty. If you haven't seen it, it's titled "ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12". You should definitely watch it, because it's really interesting. What's the problem?
The thing is, there are lots of counterintuitive results in maths and physics. There are lots of moments of wonder that our students should experience and enjoy and understand. This is potentially one of them. But the wow in this video pivots on a deceipt that is never addressed: that there is a consistent meaning of sum for a divergent sequence which corresponds either to our intuition or to our regular definition of adding.