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

[LordCalculus]

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

(\sum^{n}_{i=1} x_{i})^{2}

 

[zgozvrm]

I assume you mean:

\left(\sum_{i=1}^n x^i \right)^2

 

[zgozvrm]

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:

\sum_{i=a}^b f(x,i)

 

[zgozvrm]

For n=1, you have (x^1)^2 = x^2[/tex]<br /> <br /> For n=2, you get (x^1 + x^2)^2 = x^2 + 2x^3 + x^4[/tex]&lt;br /&gt; &lt;br /&gt; For n=3, you get x^2 + 2x^3 + 3x^4 + 2x^5 + x^6[/tex]&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; For n=4, you get x^2 + 2x^3 + 3x^4 + 4x^5 + 3x^6 + 2x^7 + x^8[/tex]&amp;amp;lt;br /&amp;amp;gt; &amp;amp;lt;br /&amp;amp;gt; &amp;amp;lt;br /&amp;amp;gt; &amp;amp;lt;br /&amp;amp;gt; Notice any pattern?&amp;amp;lt;br /&amp;amp;gt; &amp;amp;lt;br /&amp;amp;gt; Are you&amp;amp;amp;#039;re looking for the summation notation for this series, given n?