# Math Help - question about eventually decreasing sequences

1. ## question about eventually decreasing sequences

Hi everyone, I am wondering whether i got it right or wrong with this problem. If you could give me your opinion that would be great. Thanks in advance

show an example of a sequence that diverges to negative infinity but is not eventually decreasing:

i came up with this sequence: {[(-1)^n]*[2^n]} with n=1 to n= infinity. I know that this sequence isollates between one positive value and one positive value with the absolute value bigger and bigger, but I'm not sure that this sequence diverges to negative infinity. It sure diverges though.

can you suggest a better example?

2. That sequence does not diverge to negative infinity.
Consider $x_n = \left\{ {\begin{array}{ll}
{ - n ,} & \text{n even} \\
{ - 2^n ,} & \text{n odd} \\

\end{array} } \right.$

3. but doesn't that mean as n gets bigger then the sequence xn will converge to 0?