Unraveling 1999 Putnam A3: Understanding the Recurrence Relation

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Homework Help Overview

The discussion revolves around understanding a recurrence relation presented in the context of the 1999 Putnam A3 problem. Participants are examining the reasoning behind the derivation of this relation from an initial expression.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring the manipulation of an equation involving power series, questioning how to handle terms outside of summations, and discussing the conditions for equality between two power series.

Discussion Status

The conversation is active, with participants providing insights and asking clarifying questions. There is an exploration of the necessary conditions for the equality of power series, indicating a productive direction in the discussion.

Contextual Notes

Participants are grappling with the implications of having terms outside of summations and the requirements for establishing equality between power series, which may reflect constraints in their understanding of the problem setup.

ehrenfest
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Homework Statement


In the first solution to 1999 A3 at the this website:
http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1999s.pdf

You do not need to read the problem.

I do not see hot they go the recurrence relation in the first sentence. Specifically I do not follow reason why their first expression "yields the recurrence..."?

Homework Equations


The Attempt at a Solution

 
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Did you try multiplying it out and collecting like terms?
 
Yes. But you still have that one on the other side. I do not know what to do with that.
 
I'm not sure what you mean. You have an equation; the two sides are equal.
 
I am saying the 1 is outside of the summation. I need to have everything in a summation before I can get the desired result, don't I?
 
Both sides of the equation are power series. What has to be true for two power series to be equal?
 
I see. The coefficients of all powers of x greater than 0 must b 0 and the coefficient of x^0 must be 1.
 

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