I don't quite see your problem:
the function is decreasing since for .
Thus the sequence must decrease.
I tried to use the first derivative test. d/dx n^(-1/4) = -1/4 * n^(-5/4)
-1/4 * n^(-5/4) = 0
n => does not exist
If it equalled to 0 for exampel then I could show that for n>0, the output is negative but in this case, what can I do?
Any input would be greatly appreciated!
Thanks in advance!