# Define the sequence of rational numbers p(n) recursively as follows:

$p(1)=1$

$p(n)=1-\frac{p(n-1)}{2}$

• Compute and plot p(n) for $$n=1,2,\ldots , 20$$. What inference do you draw about the terms p(n)?

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# Define the sequence of rational numbers a(n) recursively as follows:

$a(1)=1$

$a(n)=\frac{1+1}{(1+a(n-1))}$

• Compute a(n) and $$a(n)^2-2$$ for $$n=1,2,\ldots , 20$$. What inference do you draw about the terms $$a(n)^2-2$$?

The graph is different with points that are increasing and decreasing. $$a(n)=\frac{1+1}{(1+a(n-1))}$$ is a horizontal line while $$a(n)^2-2$$ is a more complex solution with a different inf(a(n)) and sup(a(n)).