Proving the Equality of Newton Binomial Coefficient Using the Summation Method

[Abukadu]

Homework Statement

http://img82.imageshack.us/img82/8125/78492134fy0.th.jpg http://g.imageshack.us/thpix.php

I need to prove that the left part is equal to the right. I'm not sure how to approach the question.
I know that (n over k)=n! : k!(n-k)! but how do I sum all the number from k=0 to k=n and show that that equals to 2^n ?

 

[marlon]

Homework Statement

http://img82.imageshack.us/img82/8125/78492134fy0.th.jpg http://g.imageshack.us/thpix.php

I need to prove that the left part is equal to the right. I'm not sure how to approach the question.
I know that (n over k)=n! : k!(n-k)! but how do I sum all the number from k=0 to k=n and show that that equals to 2^n ?

use the binomial theorem and let x=y=1

marlon

 

[Abukadu]

hi marlon
what do you mean by x=y=1?
what is my x and y? the binomial theorem has r and y

 

[HallsofIvy]

What IS the binomial theorem?

 

[HallsofIvy]

We were kind of hoping that Abukadu would look it up himself! And, no, y is NOT equal to 0. If it were you would just have xⁿ= xⁿ