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

Posted on 2013-05-15
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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))
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Question by:user_n
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TommySzalapski earned 2000 total points
ID: 39167898
Start with this:
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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