Question
Determine whether the sequences in exercises are monotonic or not. Also determine whether the given sequence is bounded or unbounded.$$a_{k}=\frac{k^{2}}{k \mid}$$
Step 1
To do this, we can use the ratio test. The ratio of the $(k+1)$th term to the $k$th term of the sequence is given by: $$ \frac{a_{k+1}}{a_{k}}=\frac{(k+1)^{2}}{(k+1)!} \cdot \frac{k!}{k^{2}} $$ Simplifying this, we Show more…
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