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

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The discussion revolves around summing the series C_0^2 - 2C_1^2 + ... + (-1)^n(n+1)C_n^2, with participants expressing frustration over the complexity of the problem. Key strategies suggested include using the binomial theorem, particularly the identities (1+x)^n and (1-x)^n, and exploring the multiplication of these functions. Participants emphasize the importance of differentiating and manipulating functions to identify coefficients effectively. There is a focus on understanding how to handle the squares of coefficients in the context of series. Overall, the conversation highlights the challenges of evaluating such series and the methods to approach them.
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Homework Statement


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

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



(1+x)^n=C_0+C_1x+C_2x^2...Cnx^n
 
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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. (1-x)^n

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
(1-x)^n(1+x)^n
 

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