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 :-)
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Yep, this is what I did, too! Too hard to write in text form here...
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10
Rationalize the denominator and then you get a telescoping series.
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You must have made a small mistake in the cancellations... but telescoping series is correct indeed.
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You're right. I was doing it in my head and I started at 1 instead of 0, for some reason.
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Could it be any easier? 🤠 If I had to guess, I'd say 11.
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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.
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Actually, I didn't know! gpt said it was 11 🤠
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:)
Maybe I should wait a bit before confirming the validity of an answer in the next iterations...
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Answer given by ChatGPT for anyone wondering what it actually looks like when writing out the telescoping series.
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