
Re: D.A.P series  a new sequence of numbers
Posted:
Apr 24, 2013 10:23 AM


From: Doctor Nisith Bairagi Subject: DAP Series ? a new sequence of numbers (posted on April 20,2013 by Shyamal Kumar Das, West Bengal, India) Date: April 24, 2013 (alt.math.recreational.independent) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Dear Shyamal Babu, I have gone through your Topic on DAP keenly, and verified the arithmetic of the Problems provided.
(1) You have identified a class of AP sequence, the difference between the consecutive numbers of which is in AP. You want to call this class as: Delayed Arithmetic Progression (DAP) Series. Why <delayed> is not so clear.
(2) You have overlooked that: (1, 3, 5, 7, ), is a Sequence, and: (1 + 3 + 5 + 7 + ), is a Series. Flatly you have used the term Series, irrespective of Sequence or Series.
(3) The rule that: (DA) = 3(CB), though works well, but is obvious, and does not deserve to get special mention.
(4) You have used directly the standard solution of the sum: S<n> = 1^2 + 2^2 + 3^2 + etc = n(n + 1)(2n + 1)/6. The formula for this derivation is a standard text book one, and utilized from: n^3(n1)^3 = 3(n1)^2 + 3(n1) + 1. If you could formulate an Alternative Method of finding the sum: S<n> = 1^2 + 2^2 + 3^2 + etc, on the basis of your (proposed) Salient Features of DAP Series, it would then be called, a CONTRIBUTON. At present, the Topic appears to be a stereotype school level math exercise problem.
(5) Perhaps this class of DAP can be treated as Recurring sequence /series. A variety of such similar typical special problems for t<n> and S<n>, have already been discussed with the help of <scale of relation> concept. [Reference: Higher Algebra by Hall & Knight (1891), Chap XXIV, McMillan Co]. As I understand that, College Algebra, and Higher Algebra Books deal with similar typical complicated and harder problems. They might reveal more information in this regard.
(6) I appreciate your good amount of intelligent effort in isolating and identifying this class of Sequence / Series, as DAP. For this, credit is due to your effort. You have energized me to investigate further in this direction for opening a different gate, in generalised way.
Accept my thanks.
Doctor Nisith Bairagi Uttarpara, West Bengal, India. >>>>>>>>>>>>>>>>>>>>>>

