Determining upper and lower bounds of a sequence

[opticaltempest]

Is there a different approach I can use to determine the upper and lower bounds
of a sequence besides using the method below?

\(\displaystyle \L
a_n = ( - 1)^n \frac{1}{n}\)

\(\displaystyle \L
\left\{ { - 1,{\rm{ }}\frac{1}{2},{\rm{ }} - \frac{1}{3},{\rm{ }}\frac{1}{4}...} \right\}\)

By looking at the first few terms of the sequence I can see that it is bounded
above by 1/2 and it is bounded below by -1. Therefore the sequence is bounded.

Is there some other method I can use to determine upper and lower bounds
that doesn't require me to list out terms in the sequence?

 

[pka]

Is there some other method I can use to determine upper and lower bounds
that doesn't require me to list out terms in the sequence?

Actually, no! Finding bounds requires your knowing the behavior of the terms of the sequence. Listing the sequence out is one. But there is no single method.