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\paragraph{(a)} Show that the sequence x(n) defined recursively as follows:  \[ x(1)=1 \]  \[ x(n)=x(n-1)+1/n^2 x(n)=x(n-1)+\frac{1}{n^2}  \] is (monotone) increasing and bounded above by 2 and therefore converges.  \\Sequence x(n) or real numbers is monotone increasing if $x(n+1)\geq x(n)$ for all $n\geq 1$. Since $1+\