Dayo Ogundipe edited paragraph_Question_2_a_Show__.tex  over 8 years ago

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  Since \[ \frac{1}{n} > \frac{1}{n+1} \] for $n \geq 1$     \\x(n) naturally starts off greater and only small increments are greater. The denominator of the fraction  being added. added increases for each x(n) and x(n+1) so the sequence converges.    \\ $\therefore x(n)=\frac{1}{n}+\frac{1}{n+1}+\ldots +\frac{1}{2n}$ is monotone decreasing.