Fibonacci Numbers & the Fraction 1/89

Fibonacci sequence

Most of us are familiar with the Fibonacci Sequence. This sequence is generated by starting with 2 numbers, 1 & 1 and generating the new terms by adding 2 previous terms.
The sequence thus generated looks like
numbers in Fibonacci sequence
You will notice that we started with two numbers 1 & 1.
The new number is 1 + 1 = 2. The sequence thus becomes 1, 1, 2.
The next number is 2 + 1 = 3. The sequence thus becomes 1, 1, 2, 3.
The next number is 3 + 2 = 5. The sequence thus becomes 1, 1, 2, 3, 5.
So on...

So what is peculiar about 1/89 & this sequence?
Here goes. Lets add up the numbers of this sequence in manner shown below:
         a property of numbers in Fibonacci sequence
So, the sum looks like 0.0112359...
Now, just fire up the calculator on your computer & find out what 1/89 turns out to be.
Well, it turns out to be 0.0112359...
Interesting, isnt it?

If you are interested, feel free to go through my experiments (and results) with similar, Fibonacci-like sequences.

Fibonacci numbers appear not only in mathematics, but are ubiquitous in the nature around us. Here's where you can know more about Fibonacci numbers in Nature

To read more about Fibonacci numbers & their curious properties, here are some of the links you can visit

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