# Binomial Series

## 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 dont know what to do. Please dont ask me to give you some proof of my work at this point of time.

## Homework Equations

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

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

mjsd
Homework Helper
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 dont get is how to get the square of the coefficients.

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