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

On 30 mar, 23:45, quasi <qu...@xxxxxxxx> wrote:
On Sun, 30 Mar 2008 18:30:51 -0700 (PDT), "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 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.

(1) Find an antiderivative of the LHS.

(2) Look at the result -- do you recognize it?

(3) Based on the answer to (2), use a known formula to simplify the
result.

(4) Now differentiate the simplified result,

quasi

Hmmmmmm! This algebric trick would never happen to me wouldn't it be
your answer! Thanks a lot!

Just to be sure, the only 'induction' involved in the solution is
finding the derivative of the summation?
.

Relevant Pages

  • Re: Simplify infinite series with Sines???
    ... use a square wave as well and I'd get the same result too. ... it makes it easier to simplify; then using a saw/square wave for k=2 ... this that it is equal to a sum. ... the coefficient aof z^i in P is ...
    (sci.math)
  • Re: Problem using solve... keeps busy
    ... However, if you then simplify() the result, you get a *large* ... Then at the end of the sum, there are a few lines of other terms ... and you simplifyafter substitution (applying the ... a=x into the original equation ...
    (comp.soft-sys.matlab)
  • Re: Some questions about simplification
    ... When I try to calculate sum of ... sines or cosines, the calculator makes calculation in approximation ... SEQ SigmaLIST SIMPLIFY>> ...
    (comp.sys.hp48)
  • Re: Prolog Programming for AI, problem 7.1
    ... but have run into a nasty exercise. ... Write a procedure 'simplify' to symbolically simplify summation ... % The idea is to calculate the numeric sum, ... % a list of the atoms in the compound expression, ...
    (comp.lang.prolog)
  • Re: Simplify formula for iterative programming
    ... character set is getting munged. ... >I wondered I anybody knew about analog simplifications to simplify H: ... >This simplied formula is much easier in iterative programming, ... If, as I guessing, your H is the sum over i,j of point distances from ...
    (comp.programming)