Can't see what Ramanujan did there
If the infinite continued fraction 1 + 1 + 1 + ⋯ e − 4 π e − 2 π 1 can be expressed as e b a π ⎝ ⎛ a b + b − a c + b ⎠ ⎞ where a , b and c are coprime integers,find a + b + c .
The answer is 8.
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5 solutions
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Isn't searching the internet cheating? :)
Isnt it interesting how the golden ratio is so related to this?
Solve for the infinite continued fraction of the golden ratio, maybe it would interest you more :)
Yeah I am also interested in detailed solution! Brilliant .org should not allow uploading of any problem in the website without its detailed solution. Website Incharge please take a note of it and comment.
Well... you could take this question as a challenge for you to solve and be the first to write a detailed solution? That's what brilliant is all about.
Disagree. What use does that rule serve?
Yeah I agree with you .
"Brilliant.org should be mandatory in school"
You are so idealistic. The ideal school you are now thinking is very far from reality. You are blinded by your emotion that you failed to prioritize what/which is more important to be taught in school (maybe because you are teenager). "Brilliant.org should be mandatory in school" - is a very naive statement. In fact we don't need nerd people in our society (able to solve most complicated problem in math and science). What we need are people who are productive and useful in our society. The most important subjects/field of interest that SHOULD be taught in school are the following: VALUES, Social Studies, Humanities, Civic awareness and HUMAN relationship. Since we are human, we need to be HUMAN and HUMANE not robots. As an educator, I always internalize to my students that a successful man is not the one who is a master in science but he is the one who is a master of faith. Please be guided.
Well well, aren't you arrogant.
While I agree his statement was quite naive, but so is your statement "In fact we don't need nerd people in our society (able to solve most complicated problem in math and science). What we need are people who are productive and useful in our society. ". Imagine what the world would be like if people actually followed that. Newton, Tesla and many other important introverted people ("nerds" as you put it) have revolutionized the world with their ability to "solve complex problems". If they aren't productive people, I don't know who are. So please, if you want to rant, do it on some forum dedicated to that topic and not on a site dedicated to making people understand problems and how to approach them better so as to prepare them for future academical endeavors.
It only means that students can learn so much here that they can even have only few problems in Math. Almost everyone I met have problems in Math, including me, and Brilliant.org is one of the helpful tools.
P.S. You are right but not quite. Human relationship is useless in school, no one would listen or care enough. In my experiences, I can say that a student gains faith and improves relationships through his/her own decision making and of course - friends! Those that you have suggested would not change anyone, only he/she himself/herself could (very sad indeed D:). And I think saying that I'm only a teenager is very insulting indeed when I have experience one of the most distressing school years.
All by computing.
a = 2; b = 5 and c = 1;
Note that e^(-2 PI) is not e^(-2 Pi j) and etc. The series only need to sum up to few terms to converge to 0.998136044598509332.
In search for matching, I wrote ABS(p - q) < 5 E-6 as matching condition. Finally, I find that 5 E-19 should have been the criteria. For triple 100, exact 0 instead cannot get it.
2 + 5 + 1 = 8
well,does anyone know how to solve this question? tq :D
My knowledge of math is totally inadequate to comprehend this. But those interested may please see this: http://www.math.uiuc.edu/~berndt/articles/rrcf.pdf
P. Guerzhoy page 10.
We demand proofs!