Sum the Binomial Series: C_0^2-2C_1^2+...+(-1)^n(n+1)C_n^2

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    Binomial Series
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Homework Help Overview

The discussion revolves around summing a specific binomial series involving alternating signs and coefficients derived from binomial coefficients. The original poster expresses frustration with the problem, indicating a need to multiply series and find specific coefficients.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the nature of the series, with some clarifying that it is a partial sum rather than an infinite series. There are suggestions to express binomial coefficients in terms of n and hints involving manipulation of functions and differentiation.

Discussion Status

The discussion is active, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the manipulation of functions and the use of binomial identities, but there is no clear consensus on the next steps or a complete method.

Contextual Notes

Participants note the original poster's reluctance to provide proof of their work and express a desire for general strategies to evaluate similar series in the future. There is an underlying concern about the complexity of handling the coefficients in the series.

chaoseverlasting
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Homework Statement


Sum the following series to N terms:
[tex]C_0^2-2C_1^2+...+(-1)^n(n+1)C_n^2[/tex]

Arrgh! This is a very frustrating question. I have to multiply two series and find the coefficient of some term but I don't know what to do. Please don't ask me to give you some proof of my work at this point of time.


Homework Equations



[tex](1+x)^n=C_0+C_1x+C_2x^2...Cnx^n[/tex]
 
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Also if someone could tell me how to evaluate series of such sort in the future. I suck at this.
 
firstly, what you have been given is not a series, a series in an infinite sum.. yours is partial sum up to n. by the way it may help to write out the Cn's in terms of n.
 
hint:

1. [tex](1-x)^n[/tex]

2. look at multiplication by x, and differentiation.

3. play with functions first, then substitute in x=1
 
Last edited:
Yeah.. I did the multiplication by x and the differentiation. I already tried that. What I don't get is how to get the square of the coefficients.
 
look at coefficients in
[tex](1-x)^n(1+x)^n[/tex]
 

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