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HoldForm and Sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121769] HoldForm and Sum
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sat, 1 Oct 2011 03:07:48 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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.




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