Find the value of this infinite decimal:That is: .Code:0.01 0.001 0.0002 0.00003 0.000005 0.0000008 0.00000013 0.000000021 + ... ----------------- S = 0.011235955 ...
. . where is the Fibonacci number.
Hey Soroban. I think I may have this one. Let's see. I encountered this proof as a homework assignment back in college. In a Seminars in Mathematics course.
[tex]\frac{1}{10}\sum_{n=1}^{\infty}\frac{F_{n}}{10^{n} }[\math]
Let
Now use and we have:
So, we have:
Don't forget to multiply by our 1/10 and get: