Answer
Counting "by hand" leads us to $F(20)=6567$
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Computing the value of $F(20)$ using just the definition of the Fibonacci
the sequence would mean that we just have to write down the sequence up to
the $20^{t h}$ element. So using the knowledge:
$F(1)=1$
$F(2)=1$
$F(n)=F(n-1)+F(n-2)$ for $n>2$
we get: $1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765$
resulting $F(20)=6765$
Work Step by Step
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