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Posted on 2013-05-15

I can see that it is

1+q +q to degree of 2+q to degree of 3+...........................q to degree of (n-1)

q +q to degree of 2+q to degree of 3+...........................q to degree of (n-1)

q to degree of 2+q to degree of 3+...........................q to degree of (n-1)

.............................................................................................................

n(q to degree of (n-1))

1+q +q to degree of 2+q to degree of 3+........................

q +q to degree of 2+q to degree of 3+........................

q to degree of 2+q to degree of 3+........................

..........................

n(q to degree of (n-1))

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1 Comment

Let S = 1 + q + q^2 + q^3 + ... + q^(n-1)

Sq = q + q^2 + q^3 +q^4 + ... + q^(n-1) + q^n

But that looks pretty close to what S was. In fact:

Sq = S + q^n - 1

Now just solve

Sq - S = q^n - 1

S(q-1) = q^n - 1

S = (q^n - 1)/(q-1)

Now do the same type of thing with your equation and remember the result we just got because you will see it pop out.

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