I dont want THE continued fraction because it's not formed as a sum of infinite series. Also, when I try to make it as such, its 2nd, 4th, 6th and so on terms are greater than √2, e.g. the fourth term is 1+(5/12), so I guess it's not what I want, but I might be wrong.
I dont want THE continued fraction because it's not formed as a sum of infinite series. Also, when I try to make it as such, its 2nd, 4th, 6th and so on terms are greater than √2, e.g. the fourth term is 1+(5/12), so I guess it's not what I want, but I might be wrong.
Your last words seem to imply that you're not really sure either of what you
want or else you're not quite sure what you were asked to do: the "something with n in it" is numbers in
the examples you've been given, and the n only serves as counting index.
A simple way to achieve what you want is:
Tonio
Let's say that I want something like the 1+2(1/8)+4(1/8)^2+8(1/8)^2+...of the area of the parabola
Geometric series - Wikipedia, the free encyclopedia
where instead of the area of the parabola, it is the side √2 of a triangle with sides 1,1,√2. So, none of the terms of the sum can be greater than √2. What I mean by "the terms of the sum" is for example regarding the continued fraction:
first term = 1
second term = 1+1/2
third term = 1+(1/(2+(1/2))=1+(2/5)
Square_root_of_2
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