Sum the series of alternating binomial coefficient squares

[chaoseverlasting]

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

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

 

[chaoseverlasting]

Also if someone could tell me how to evaluate series of such sort in the future. I suck at this.

 

[mjsd]

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.

 

[tim_lou]

hint:

1. $$(1-x)^n$$

2. look at multiplication by x, and differentiation.

3. play with functions first, then substitute in x=1

 

[chaoseverlasting]

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.

 

[tim_lou]

look at coefficients in
$$(1-x)^n(1+x)^n$$