Question

The Fibonacci sequence is defined by $1=a_1=a_2$ and $a_n=a_{n-1}+a_{n-1},n>2$.
Find $\frac{a_n}{a_n+1}$ for $n=1,2,3,4$.

Answer 1

$a_1=a_2=1$

$a_n=a_{n-1}+a_{n-1}$

find $\frac{a_n}{a_n+1}$

a) $n=1\Rightarrow \frac{a_1}{a_1+1}=\frac{1}{1+1}=\frac{1}{2}$

b) $n=2\Rightarrow \frac{a_2}{a_2+1}=\frac{1}{1+1}=\frac{1}{2}$

c) $n=3\Rightarrow \frac{a_3}{a_3+1}=\frac{2}{2+1}=\frac{2}{3}$

d) $n=4\Rightarrow \frac{a_4}{a_4+1}=\frac{3}{3+1}=\frac{3}{4}$.