# Summation Notation.

## Main Question or Discussion Point

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

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

I assume you mean:

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

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:

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

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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?