#1
Trott-Strzebonski in-place evaluation:
hf = HoldForm[1 - 1^2/2 + 1^3/3 - 1^4/4 + 1^5/5 - 1^6/6]
hf /. x_Times :> With[{eval = x}, eval /; True]
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6
Replace[hf, x_ :> With[{eval = x}, eval /; True], {2}]
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6
One may simplify this method using the undocumented function RuleCondition
as WReach showsWReach shows:
Replace[hf, x_ :> RuleCondition[x], {2}]
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6
#2
Injector patternInjector pattern:
{1, -(1/2), 1/3, -(1/4), 1/5, -(1/6)} /. {x__} :> HoldForm[+x]
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6