       Re: Series holding the final sum

• To: mathgroup at smc.vnet.net
• Subject: [mg117783] Re: Series holding the final sum
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 31 Mar 2011 04:02:40 -0500 (EST)

```Jon Joseph wrote:
> All:  Given the following sum:
>
> Sum[(-1)^(n + 2) x^(2 n + 1)/(2 n + 1), {n, 0, 5}]
>
> which generates:
>
> x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - x^11/11
>
> I would like to replace x with -1 (%/.x->-1) without the sum being evaluated so I end up with
>
> -1+1/3-1/5+1/7-1/9+1/11
>
> So far I have not been able to find a way to Hold, HoldForm, Unevaluate, or Defer and keep getting -2578/3465.  Thanks. Jon=
>

Here is one method. We replace Plus by plus and define special
formatting for the latter.

In:= plus /: MakeBoxes[plus[x_], StandardForm] := MakeBoxes[x]
plus /: MakeBoxes[plus[x_, y_], StandardForm] :=
RowBox[{MakeBoxes[x, StandardForm], "+",
MakeBoxes[y, StandardForm]}]
plus /: MakeBoxes[plus[x_, y_, z__], StandardForm] :=
RowBox[{MakeBoxes[plus[x, y], StandardForm], "+", MakeBoxes[plus[z]]}]

In:= ss = Sum[(-1)^(n + 2) x^(2 n + 1)/(2 n + 1), {n, 0, 5}];
ss2 = ss /. Plus -> plus /. x -> -1

Out= (-1 + 1/3) + ((-(1/5) + 1/7) + (-(1/9) + 1/11))

Daniel Lichtblau
Wolfram Research

```

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