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Binomial Series

  • #1

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 dont know what to do. Please dont 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]
 

Answers and Replies

  • #2
Also if someone could tell me how to evaluate series of such sort in the future. I suck at this.
 
  • #3
mjsd
Homework Helper
726
3
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
682
1
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:
  • #5
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
682
1
look at coefficients in
[tex](1-x)^n(1+x)^n[/tex]
 

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