Often it is preferable to use Module[]
:
powersum[x_,p_]:=Module[{sum},sum=0;For[i=1,i<x,i++,sum=sum+i^p];sum]
or
powersum[x_,p_]:=Module[{sum=0},For[i=1,i<x,i++,sum=sum+i^p];sum]
this is essentially the same as wrapping in ()
except sum
is protected in a local context.
of course for this example you could as well use :
powersum[x_,p_]:=Sum[i^p,{i,1,x-1}]
or
powersum[x_, p_] := Range[x - 1]^p // Total