Question

Fun question

Answer 1

type faster! XD

Answer 2

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

Answer 3

OOOOO the answer is...... something :D am i right?

Answer 4

is that u tash?

Answer 5

Who else would be this smart

Answer 6

*giggels* XD

Answer 7

XD I know what seba looks like....

Answer 8

Yah..... that question is way to hard..... Is it Calculus?

Answer 9

\[\sum_{n=0}^\infty F_nx^n = \frac{1}{1-x-x^2}\]

plugin \(x = \frac{1}{2}\)

Answer 10

:D do u knw the derivation of this thing? :)

Answer 11

derivation is pretty easy, there are hundreds of web pages that has this derivation...

Answer 12

http://math.stackexchange.com/questions/338740/the-generating-function-for-the-fibonacci-numbers?lq=1

Answer 13

i'll post a better fun question @ganeshie8 aka geniusie8

Answer 14

:D

Answer 15

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.

Answer 16

thanks @ganeshie8

Answer 17

Hey, I posted that on PA.

Answer 18

lol

Answer 19

\[\lim_{n \to \infty } \frac{F_{n+1}}{F_n} = L \]\[= \lim_{n\to \infty} \frac{F_n}{F_n} + \lim_{n \to \infty} \frac{F_{n-1}}{F_n}\]\[= 1 + \frac{1}{L}\]