Re: HoldForm and Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg121793] Re: HoldForm and Sum
• From: "Tong Shiu-sing" <sstong at phy.cuhk.edu.hk>
• Date: Mon, 3 Oct 2011 04:19:55 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110010707.DAA17769@smc.vnet.net>

```Hello,

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

----- Original Message -----
From: "dimitris" <dimmechan at yahoo.com>
To: <mathgroup at smc.vnet.net>
Sent: Saturday, October 01, 2011 3:07 PM
Subject: [mg121793] HoldForm and Sum

> 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.
>