Unevaluated Sum of a sequence

Questions
1

How can I get mathematica to write out a sum without evaluating it immediately eg

Sum[3^i,{i,1,10}]

I want to get the following first 3^1+3^2+3^3+…3^10 without having to input each term separately.

2

A first attempt:

Inactive[Plus] @@ Table[Inactive[Power][3, i], {i, 10}]
3

@Gianluca Gorni you could simplify your version to

Sum[Inactive[Power][3, i], {i, 1, 10}]

If @RAY LAWICKI wants nice typesetting this could work:

Sum[Superscript[3, i], {i, 1, 10}]

with further evaluation triggered as

% /. Superscript -> Power
4

THANKS,for the response but can I have the following Sum[Superscript[I!, 2], {i, 1, 5}] write out the sequence as a factorial first.
, because it responds with1^2+2^2+6^2+24^2+120^2 rather than ( 1!)^2+(2!)^2+(3!)^2+…

5

Plus @@ Table[Inactive[Factorial][i]^i, {i, 10}]

6

thanks for the hint however it does not produce + signs between the elements ,what I wanted was an output as ( 1!)^1+(2!)^2+(3!)^3+(4!)^4… help
ray

7

The plus signs show up fine on my system (Mma version 10.3.1). What version are you on?

8

MY MATHEMATICA IS VERSION 10.0 AND IT DOES WORK FINE BECAUSE I JUST REALISED THAT I WAS USING && RATHER THAN @@ SO THANKS AGAIN. Can you explain how that code works as I don’t understand the use of @@ in the line and why I cannot use I! rather the the word factorial. Also I am trying to plot a series of separate graphs in different colour but my code is not working correctly eg I define f(x)=x^2-x+3 (say) ,then Table[Plot[f,{x,-6,6},PlotRange->10],{f,[f(x],f[2x],f[x-2],-2f{x]}}] which produces a table of the graphs but if I now include PlotStyle->{Red,Green,Blue,Orange} I get no graphs.
ray.

9

The command Table[Inactive[Factorial][i]^i, {i, 10}] produces a List[ 1!, 2!, ...]. What I want is Plus[ 1!, 2!, ...]. The prefix Plus@@ does precisely that: it replaces List with Plus.

10

This seem to work

f[x_]:=x^2-x+3;
Plot[#2,{x,-6,6},PlotRange->10,PlotStyle->#1]&@@@{{Red,f[x]},{Green,f[2 x]},{Blue,f[x-2]},{Orange,-2f[x]}}
11

thanks I understand the use of@@
ray

12

thanks it does work but I do not understand the following bits of the code #2 what does this do and &@@@ what does this mean and why do we have #1 in plotstyle?
being only a beginner I some times do not understand the effect of the above.
ray.

13

The operators @@ and @@@ are shorthands for two forms of Apply, which is a structural manipulation function. They work on the special way Mathematica expressions are built: they are of the form h[x,y,…], where h is the “head” of the expression. The function Apply replaces the heads of expressions with other heads:

f@@h[x,y,…] gives f[x,y,…] (top level replacement)

f@@@h[g[x],g[y],…] gives h[ f[x], f[y],…] (lower level replacement)

The & operator indicates that what comes before it is a “pure function”, whose arguments are indicated with #, or #1,#2,…

It is not uncommon to find & immediately followed by @@ or @@@, but they are distinct objects.

14

You could write

f[x_] := x^2 - x + 3;
Plot[#[[2]], {x, -6, 6}, PlotRange -> 15,    PlotStyle -> #[[1]]] 
& /@ {{Red, f[x]}, {Green, f[2 x]}, {Blue,    f[x - 2]}, {Orange, -2 f[x]}}

as well, if you prefer to use /@ instead @@@. /@ is the shortcut for Map[ ] and applies the function to each element of first level in the list. Here each of these elements will be a list again such as{Red, f[x]}.

By the way: Simply writing #1 and #2 won’t be succesfull. You need the subscription given by the brackets [[ ]].

15

Unevaluated Sum of a sequence

16

thank you for your suggestion
ray.

17

I am having some problem with complex number as shown in the attached file.
ray

18

I think there is no built-in function for exactly the thing you need. The closest is AbsArg. You can build the exponential from there:

AbsArg[2 - 2 I] /. {r_, t_} :> r*Exp[I*t]
Abs[2 - 2 I] Exp[I*Arg[2 - 2 I]]

You can define your own function:

ConvertToExponential[z_] := Abs[z] Exp[I*Arg[z]]
19

Returning to the original question—and letting the sum run from 1 to 100 to give a result where you would indeed want an ellipsis (dots) rather than the whole sum&mdash: This sort of thing is nicely handled by the EllipsisSequences package that is just one small part of David Park’s Presentationa application:

     <<Presentations`
     iSum[Inactivate[3^i], {i, 1, 2, 3, , i, , 100}]
3^1 + 3^2 + 3^3 + ... + 3^i + ... + 3^100

Although Park has offered a no-cost version of Presentations without the documentation as well as the complete application with documentation, unfortunately at present the link to his web page on that seems dead.

20

You can try this way:

Inactive[Plus] @@ 
 Table[Inactive[Power][3, 
   i], {i, {1, 2, 3, \[CenterEllipsis], i, \[CenterEllipsis], 100}}]