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zmudz
 one year ago
A sequence of real numbers (x_n) is defined recursively as follows: x_0=a and x_1=b are positive real numbers, and x_{n + 2} = (1 + x_{n + 1})/(x_n) for n = 0, 1, 2, .... so on. Find the value of x_{2012}, in terms of x_0 and x_1. Thanks!
zmudz
 one year ago
A sequence of real numbers (x_n) is defined recursively as follows: x_0=a and x_1=b are positive real numbers, and x_{n + 2} = (1 + x_{n + 1})/(x_n) for n = 0, 1, 2, .... so on. Find the value of x_{2012}, in terms of x_0 and x_1. Thanks!

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danica518
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437194441049:dw

danica518
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437194518228:dw

danica518
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437194651461:dw

danica518
 one year ago
Best ResponseYou've already chosen the best response.2im not seeing a trick, maybe its one of those continued fraction tricks?

danica518
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437194858049:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the sequence starts to repeat itself starting at x_5

danica518
 one year ago
Best ResponseYou've already chosen the best response.2should i simplify X3 and X4 or can i leave it all in that form

freckles
 one year ago
Best ResponseYou've already chosen the best response.1simplifying helps to see the pattern

danica518
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437195330961:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[x_4=\frac{1+\frac{a+b+1}{ab}}{\frac{1+b}{a}} \\ \text{ multiply top and bottom by } ab \\ \\ x_4=\frac{ab +a+b+1}{b(1+b)}=\frac{a(b+1)+(b+1)}{b(b+1)} \\ x_4=\frac{(b+1)(a+1)}{b(b+1)}=\frac{a+1}{b}\]

zmudz
 one year ago
Best ResponseYou've already chosen the best response.0That answer isn't right, and I'm not sure why because it makes sense to me... I don't know the answer but my homework is telling me it is wrong.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the sequence is an example of one in rank2 cluster algebras; it has a period of 5 for any initial values, so $$x_{2012}=x_{20122010}=x_2$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and we have $$x_2=\frac{1+x_1}{x_0}=\frac{1+b}a$$
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