Re: (Discrete Math - Induction) 'Formula Differentiation'

On Mar 30, 6:30 pm, "almeidabati...@xxxxxxx"
<almeidabati...@xxxxxxxxx> wrote:
Hi all! I've got this problem in my set:

'1 + 2q + 3q^2 + ... + nq^(n-1) = [1 - (n+1)q^n + nq^(n-1)]/[(1 -
q)^2], q <> 1.

Estabilish [the formula above] by differentiating the expansion of the
formula for the sum of a geometric progression.'

I've been thinkering

Well, you can be 'tinkering' or 'thinking', but 'thinkering' is a new
one on me. I like it!

with this one all day, no clue on how to start.
ANY hints on how the derivative of the sum of terms of a G.P will get
into this are welcome.

Write down the formula for the sum of a geometric progression; the
left-hand-side should be 1 + q + q^2 + ... + q^n, while the right-hand-
side should be the formula you get after summing (that is, [1 - q^(n
+1)]/(1-q)). Now differentiate the left-hand-side. What do you get?
Differentiate the right-hand-side. What do you get? You see, this just
carries out the instructions that you were given in the question.

R.G. Vickson
.

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