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 [itex](x^1)^2 = x^2[/tex]

For n=2, you get [itex] (x^1 + x^2)^2 = x^2 + 2x^3 + x^4[/tex]

For n=3, you get [itex]x^2 + 2x^3 + 3x^4 + 2x^5 + x^6[/tex]

For n=4, you get [itex]x^2 + 2x^3 + 3x^4 + 4x^5 + 3x^6 + 2x^7 + x^8[/tex]



Notice any pattern?

Are you're looking for the summation notation for this series, given n?

 

[CellCoree]

The result of this in summation notation after multiplying it out would be represented as:

\sum^{n}_{i=1} x_{i}^{2} + \sum^{n}_{i=1} \sum^{n}_{j=1} x_{i}x_{j}