Re: HoldForm and Sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg121783] Re: HoldForm and Sum*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>*Date*: Sun, 2 Oct 2011 02:35:41 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j66e8v$hbs$1@smc.vnet.net>

"dimitris" <dimmechan at yahoo.com> schrieb im Newsbeitrag news:j66e8v$hbs$1 at smc.vnet.net... > Hell to all. > > A (well-known) nice example of the use of HoldForm is: > > Sum[(HoldForm[#1] & )[i], {i, 1, 10}] > > (*output omited*) > > I want to do the same with 1/i > > Sum[(HoldForm[#1] & )[1/i], {i, 1, 10}] > > Mathematica output is > > 1/10+1/9+1/8+...+1/3+1/2+1 > > My first question is how can I get the output in the form > > 1+1/2+1/3...+1/8+1/9+1/10 > > > My second query comes now. How can I combine HoldForm and Sum (or > anything else) in order to have the following output (unevaluated)? > > 1+1/2+1/3-1/4-1/5-1/6+1/7+1/8+1/9-1/10-1/11-1/12 > > that is, three positive terms after three negative and so on. > > Thank you in advance for your response. > > These two sums do what you want (except for the "ugly" 1/1) s1 = Sum[HoldForm[1/#] & [i], {i,1, 10}] (* 1/# rather than [1/i] *) 1 1 1 1 1 1 1 1 1 1 - + - + - + - + - + - + - + - + - + -- 1 2 3 4 5 6 7 8 9 10 s2 = Sum[(-1)^Floor[(k-1)/3]HoldForm[1/#]&[k],{k,1,12}]//OutputForm 1 1 1 1 1 1 1 1 1 1 1 1 - + - + - - - - - - - + - + - + - - -- - -- - -- 1 2 3 4 5 6 7 8 9 10 11 12 Wolfgang