Nice puzzle, with simple rewriting the fraction we can get all denominators equals to 1 and then we will get the telescope... So, the sum is equals to \sqrt{121} - \sqrt{0} = 11 :-)
Yeah, this one is pretty easy, especially if you went through some basic math courses. As I plan on doing this daily, proper difficulty and fun-factor will be hit or miss.
I also just put it in ChatGPT, it properly reasons and gives the intermediate steps to get to this correct final result.
Nice puzzle, with simple rewriting the fraction we can get all denominators equals to 1 and then we will get the telescope... So, the sum is equals to \sqrt{121} - \sqrt{0} = 11 :-)
Yep, this is what I did, too! Too hard to write in text form here...
Could it be any easier? 🤠If I had to guess, I'd say 11.
Your educated guess is correct.
Yeah, this one is pretty easy, especially if you went through some basic math courses. As I plan on doing this daily, proper difficulty and fun-factor will be hit or miss.
I also just put it in ChatGPT, it properly reasons and gives the intermediate steps to get to this correct final result.
Actually, I didn't know! gpt said it was 11 ðŸ¤
:)
Maybe I should wait a bit before confirming the validity of an answer in the next iterations...
10
Rationalize the denominator and then you get a telescoping series.
You must have made a small mistake in the cancellations... but telescoping series is correct indeed.
You're right. I was doing it in my head and I started at 1 instead of 0, for some reason.
Answer given by ChatGPT for anyone wondering what it actually looks like when writing out the telescoping series.
@remindme in 12 hours