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\paragraph{(h)} Do you think the sequence x(n) converges? If so, why, and if not, why not?  The sequence x(n) does converge at an estimated value of $x(n) = 1\frac{2}{3}$. I think this because as n increases to $\infty$ the values of x(n) get closer to the value $1\frac{2}{3}$. If we look at the graph it becomes more horizontal close to a straight line at $x(n) = 1\frac{2}{3}$. \paragraph{(i)} Prove, by induction, that $\vert x(n+1)-x(n)\vert = 1/2^{n-1}$ for all $n\geq 2$.