# Binomial Series

1. Mar 19, 2007

### chaoseverlasting

1. The problem statement, all variables and given/known data
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 dont know what to do. Please dont ask me to give you some proof of my work at this point of time.

2. Relevant equations

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

2. Mar 19, 2007

### chaoseverlasting

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

3. Mar 19, 2007

### 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.

4. Mar 19, 2007

### 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

Last edited: Mar 19, 2007
5. Mar 20, 2007

### chaoseverlasting

Yeah.. I did the multiplication by x and the differentiation. I already tried that. What I dont get is how to get the square of the coefficients.

6. Mar 20, 2007

### tim_lou

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