How to Write the Result of a Squared Summation Notation After Multiplication?

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Discussion Overview

The discussion revolves around expressing the result of a squared summation notation, specifically \((\sum^{n}_{i=1} x_{i})^{2}\), after multiplying it out. Participants explore the implications of this notation and seek to clarify its representation in summation form.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks how to write the result of \((\sum^{n}_{i=1} x_{i})^{2}\) in summation notation after multiplication.
  • Another participant suggests a potential interpretation of the notation as \(\left(\sum_{i=1}^n x^i \right)^2\).
  • Another response asserts that the expression is already in summation notation and questions whether the intent is to find a non-squared summation equivalent.
  • Further contributions provide specific examples for small values of \(n\), showing the expanded forms for \(n=1\) to \(n=4\) and prompting others to identify patterns in the results.
  • Participants inquire if the goal is to derive a summation notation for the resulting series based on the value of \(n\).

Areas of Agreement / Disagreement

There is no clear consensus on whether the original expression is sufficient as is or if a different form is desired. Multiple interpretations and approaches are presented without resolution.

Contextual Notes

Participants have not explicitly defined the terms or conditions under which the summation notation should be transformed, leading to potential ambiguity in the discussion.

LordCalculus
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How would I write the result of this in summation notation after multiplying it out?

([tex]\sum[/tex][tex]^{n}_{i=1}[/tex] x[tex]_{i}[/tex])[tex]^{2}[/tex]
 
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I assume you mean:

[tex]\left(\sum_{i=1}^n x^i \right)^2[/tex]
 
It already is in summation notation!

(or, are you trying to come up with a summation equal to this, in which the result is not squared?)


in the form of:

[tex]\sum_{i=a}^b f(x,i)[/tex]
 
Last edited:
For n=1, you have [itex](x^1)^2 = x^2[/tex]<br /> <br /> For n=2, you get [itex](x^1 + x^2)^2 = x^2 + 2x^3 + x^4[/tex]<br /> <br /> For n=3, you get [itex]x^2 + 2x^3 + 3x^4 + 2x^5 + x^6[/tex]<br /> <br /> For n=4, you get [itex]x^2 + 2x^3 + 3x^4 + 4x^5 + 3x^6 + 2x^7 + x^8[/tex]<br /> <br /> <br /> <br /> Notice any pattern?<br /> <br /> Are you're looking for the summation notation for this series, given n?[/itex][/itex][/itex][/itex]
 

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