'The nth Fibonacci number'. Is it the actual '9th' number(55) or the sum of the ninth Fibonacci sequence(144)? Fiddling around with Rust in Emacs,today. Rust Book suggests 'tasks' to accomplish. Came across this in a tutorial vid. Having a lot of fun.

Bold choice for a coding font

Regarding the question which one exactly the "ninth" Fibonacci number is, that might be just a matter of convention. Usually people start the Fibonacci numbers either `1, 1, 2, 3, 5, 8, ...`

or `0, 1, 1, 2, 3, 5, ...`

. However, when starting with `0`

, you could also give the initial `0`

the index `0`

; i.e. you could generally define for indices *i* the number *F*_{i} so that

F= 0_{0}

F= 1_{1}

F= 1_{2}

F= 2_{3}

F= 3_{4}

F= 5_{5}

F= 8_{6}

F= 13_{7}

F= 21_{8}

F= 34_{9}

...and so on

but then again, we could discuss whether to call *F _{0}* the "first" Fibonacci number or the "zeroth" Fibonacchi number (which matters for the ninth one, too, if you count further up). Talking about zero-based indexing in plain English really is not trivial. In conclusion, when asking for ninth Fibonacci number, you would most commonly either be referring to

*F*= 34, or possibly to

_{9}*F*= 21.

_{8}Side note: A good reason for choosing the indices *F _{0}*,

*F*, etc.. precisely the way it's done above is that this convention allows for a clean general closed-form formula

_{1}*Edit: Formula in grey supports light theme and dark theme *

You want the numbering where F_{0} is 0; there are many other formulas involving Fibonacci numbers such as "F_{kn} is a multiple of F_{n}" that rely on it.

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