The discussion revolves around proving the equality of two expressions involving the binomial coefficient, specifically showing that the summation of binomial coefficients from k=0 to n equals 2^n. The subject area is combinatorics and the binomial theorem.
The discussion is ongoing, with participants exploring different interpretations of the binomial theorem and its application. There is a lack of consensus on the definitions and the approach to take, but some guidance has been offered regarding the use of the binomial theorem.
Participants note that there may be confusion regarding the variables used in the binomial theorem, and there is an expectation for the original poster to engage with the material independently.
Abukadu said: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 ?