Gaah.
Can someone please tell me the value of this fraction. (Pretend it goes infinitely.)
Conversation
Replying to
Worked at it for five minutes and got nowhere. Where did you get this from?
1
Replying to
I made it up. It seems to converge to rt(3) which kind of makes sense because rt(3)=1+(1+rt(3))/(2+rt(3)) but there's a problem:
1
Replying to
That logic implies that the numerator, 1+rt(3), should equal 2+(3+rt(3))/(5+rt(3)) and it doesn't.
1
Replying to
But (3+rt(3))/(5+rt(3)) = (4+(1+rt(3))/(2+rt(3)))/(6+(1+rt(3))/(2+rt(3))), which should fit, no?
1
Replying to
I'm not sure what you mean. Are you saying it is in fact rt(3)? If instead you're saying the proof doesn't work, then I agree.
1
Replying to
I think that the proof does work. You just need to keep hacking through.
1
Replying to
Therefore, the numerator 1+r3 = (4+(1+r3)/(2+r3))/(6+(1+r3)/(2+r3)), which seems to fit the pattern required.
1
Replying to
But 1+r3 doesn't equal (4+(1+r3)/(2+r3))/(6+(1+r3)/(2+r3)).
1+r3 = 2.732
2+(4+(1+r3)/(2+r3))/(6+(1+r3)/(2+r3)) = 2.702
Translate Tweet
Replying to
Oh, that's what you meant by "that logic implies etc." Give me a moment to think this out...
1