2:28 hmmm, that wasn't where I was expecting you to go with this. I was expecting the explanation "1/(x + 2022) is a large number, so x + 2022 must be a small decimal. Adding 1, we get that x + 2023 must be a bit more than 1. So its reciprocal must be a bit less than 1."
You can tell from just the initial equation that the amount in the denominator must equate to 1/2022, so of course adding or subtracting just one from x will shift it away from there being a miniscule fraction in the denominator, making the overall fraction much smaller.
![The Easiest Problem on the Hardest Test [2017 Putnam Competition A1]](http://i.ytimg.com/vi/9M4fBKKEndw/mqdefault.jpg)
![The Easiest Problem on the Hardest Test [2017 Putnam Competition A1]](/img/tr.png)
2:28 hmmm, that wasn't where I was expecting you to go with this. I was expecting the explanation "1/(x + 2022) is a large number, so x + 2022 must be a small decimal. Adding 1, we get that x + 2023 must be a bit more than 1. So its reciprocal must be a bit less than 1."
that's a great way to think about it!
there are 2 Points where f(x+1)=f(x)±1
I only have a graphical proof butbit is always possible
You can tell from just the initial equation that the amount in the denominator must equate to 1/2022, so of course adding or subtracting just one from x will shift it away from there being a miniscule fraction in the denominator, making the overall fraction much smaller.
2022/2023. Did it in my head.
Was an easy enough problem, but I can see why you deemed it video-worthy.
was expecting to see some complex graph at the end to find the two points but that was a fun little exploration
Can you try to solve questions from competitive exams in India LIKE SSC CGL ETC. GENUINELY NEED
Thanks!
You’re too kind. I needed the encouragement today :)
Why is this video 10 minutes long when it takes
Lol. “Why do we have to throw a whole party, it only takes 30 seconds to sing Janet the birthday song!?!”
legends will say 2023
lol