You can change the attributes of Plus to achieve the forms:
Unprotect[Plus]
ClearAttributes[Plus, Orderless]
Sum[(HoldForm[#1] &)[1/i], {i, 1, 10}]
gives
1+1/2+1/3...+1/8+1/9+1/10
Sum[((-1)^Quotient[i - 1, 3] HoldForm[#1] &)[1/i], {i, 1, 12}]
gives
1+1/2+1/3-1/4-1/5-1/6+1/7+1/8+1/9-1/10-1/11-1/12
Hope this is useful.
Regards,
Dominic