Sum of Consecutive Powers I am trying to understand a cross between steps when finding the formula for the sum of consecutive powers.
I am following the steps from a webpage here http://mikestoolbox.com/powersum.html but will also provide them below:
Step 1: Sum = x^5 + x^4 + x^3 + x^2 + x + 1
Step 2: Sum · x + 1 =   x^6 + x^5 + x^4 + x^3 + x^2 + x + 1
=   x^6 + (x^5 + x^4 + x^3 + x^2 + x + 1)
=   x^6 + Sum

Step 3: Rearranging the above equation we can then get:
Sum · (x − 1) = x^6 − 1
I am missing some very basic math knowledge that is blocking me from understanding how he is getting from step 2 to step 3. I.e how is he going from Sum * x + 1 = x^6 + Sum to the following step
Sum * (x-1) = x^6 - 1

You do not need to add 1 after multiplying with $x$.
$$S=1+x+x^2+\ldots+x^n$$
$$xS=x+x^2+\ldots+x^n+x^{n+1}$$
Subtract both equations:
$$S(1-x)=1-x^{n+1}$$
