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\paragraph{(a)} Show that the sequence x(n) defined recursively as follows:  \[ x(1)=1 \]  \[ x(n)=x(n-1)+\frac{1}{n^2} x(n)=x(n-1)+ \frac{1}{n^2}  \] is (monotone) increasing and bounded above by 2 and therefore converges.