For

, there are no skips in the alternations of the partial sums. In order to have such a skip, there must be a sign change between

and

. This is equivalent to having exactly one root of

in

. It can be shown that this happens for

. For

we still have two real roots to this equation, but both are in the interval

. Hence there is no sign change (because there were two skips within the same unit interval). For

, there are no longer real solutions to the equation

. Also notice that for

, we have a root for

and another with

. Hence we have consecutive sign changes. For

in this range, we have an initial sequence of three partial sums decreasing after the first term.