imqwerty
  • imqwerty
Fun question
Mathematics
chestercat
  • chestercat
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Hayleymeyer
  • Hayleymeyer
type faster! XD
imqwerty
  • imqwerty
originally posted by @ParthKohli Find the value of \[\sum_{n=1}^{\infty}\frac{F(n)}{2^n}\] where F(n)=n th term of fabronici series
anonymous
  • anonymous
OOOOO the answer is...... something :D am i right?

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Hayleymeyer
  • Hayleymeyer
is that u tash?
anonymous
  • anonymous
Who else would be this smart
Hayleymeyer
  • Hayleymeyer
*giggels* XD
anonymous
  • anonymous
XD I know what seba looks like....
anonymous
  • anonymous
Yah..... that question is way to hard..... Is it Calculus?
ganeshie8
  • ganeshie8
\[\sum_{n=0}^\infty F_nx^n = \frac{1}{1-x-x^2}\] plugin \(x = \frac{1}{2}\)
imqwerty
  • imqwerty
:D do u knw the derivation of this thing? :)
ganeshie8
  • ganeshie8
derivation is pretty easy, there are hundreds of web pages that has this derivation...
ganeshie8
  • ganeshie8
http://math.stackexchange.com/questions/338740/the-generating-function-for-the-fibonacci-numbers?lq=1
imqwerty
  • imqwerty
i'll post a better fun question @ganeshie8 aka geniusie8
imqwerty
  • imqwerty
:D
ganeshie8
  • ganeshie8
questions relating to fibonacci sequence are fun indeed! try this when you're free : \[\large \lim\limits_{n\to\infty}\dfrac{F_{n+1}}{F_n} ~~=~~\phi\] where \(\phi\) is the golden ratio.
imqwerty
  • imqwerty
thanks @ganeshie8
ParthKohli
  • ParthKohli
Hey, I posted that on PA.
imqwerty
  • imqwerty
lol
ParthKohli
  • ParthKohli
\[\lim_{n \to \infty } \frac{F_{n+1}}{F_n} = L \]\[= \lim_{n\to \infty} \frac{F_n}{F_n} + \lim_{n \to \infty} \frac{F_{n-1}}{F_n}\]\[= 1 + \frac{1}{L}\]

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