Answer
The first algorithm is easy to understand but takes a lot of steps for big
numbers like $\mathrm{F}(100) .$ The second one provides us with a shortcut and any
value can be found just by plugging in the value for $n$ in the formula.
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The first algorithm is most easily understood since it involves the simplest
operation - addition. However, it is not as elegant and efficient as the second
one, since it takes up a lot of time if it is not done using a computer.
But even considering using a computer, the second algorithm, which involves
a known formula, would be far superior in terms of efficiency, especially when
looking at greater values like $F(100) .$
It is important to note, that you will hardly get an integer after performing
the calculations for the second algorithm on a calculator. You will be
limited to the number of digits that your calculator can display. It will
look something like this most of the time 6567.000$\ldots $.
Work Step by Step
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