It’s not split in half, it’s reversed, which is why both are equal to S. If you just took half, then 1 + 2 + … would not equal 100 + 99 + … and so they both wouldn’t be equal to S.
Instead of halving the list, they just reversed it and summed it to 2S later, which they then half. So no typo here.
It’s not split in half, it’s reversed, which is why both are equal to S. If you just took half, then 1 + 2 + … would not equal 100 + 99 + … and so they both wouldn’t be equal to S.
Instead of halving the list, they just reversed it and summed it to 2S later, which they then half. So no typo here.
I had the same reaction originally though, because I feel like I had seen this previously as just “bending” the list of 1-100 in half.
1+2+3+4+...+49+50 100+99+98+97+...+52+51 = 101+101+101+...101 * 50.
So you have to do a bit more thinking to define your equation but the equation takes you straight to S instead of 2S.
And since the meme just has
+ ...instead of showing where the end of the list was, I see how one could easily mix up the 2 approaches.