As ratio and root tests fail you have to use comparison to prove that this series converges (which does not mean that you now know what it converes to).
To evaluate that kind of series with Mathcad you have to use symbolic evaluation, not the numeric one you tried
Unfortunately Mathcads symbolics isn't capable to deal with your series. The results are different whether you force float mode (using 0.5) or exact mode (using 1/2), but not helpful in either case.
Mathcad is generally not really good with that kind of symbolics. While it knows about this series and successfully yields the Rieman Zeta as result
it isn't even able to deal with this (equivalent) series
