# How do I show that 1/n^(1/4) is decreasing?

• May 4th 2010, 09:49 AM
s3a
How do I show that 1/n^(1/4) is decreasing?
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!
the function $f(x)= x^{-1/4}$ is decreasing since $f'(x)=-\frac{1}{4}x^{-5/4} < 0$ for $x> 0$.
Thus the sequence $x_n =n^{-1/4}$ must decrease.