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 tonegativeinfinity. It sure diverges though.

can you suggest a better example?