For the series, determine if it's okay to use the integral test. If so, use the integral test to determine whether the series converges or diverges.
is non-negative and decreasing on [1,∞). From ancient history we know that since 0.5 < 1 the integral
diverges. The integral test tells us that the series
must also diverge.
The shorter version is that we could use the p-test for series to say that since
p = 0.5 < 1
we know by the p-test that the series diverges.