I need help in my mathematical reasoning class!

[abaker]

the question that I CANNOT figure out is this:
explain why 2^n = (n choose 0) + (n choose 1) + (n choose 2) + ... + (n choose n-1) + (n choose n)

so far my work is:
(n choose 0) = n!/0!n= 1
(n choose 1) = n
(n choose 2) = (-n)2/2!=1/2(n-1)n
(n choose n-1) = n!/1!(-1+n)! = n
(n choose n) = n!/0!n = 1
I don't know if I am approaching this the right way or how to approach this kind of question

thanks for any help!

 

[burakaltr]

the question that I CANNOT figure out is this:
explain why 2^n = (n choose 0) + (n choose 1) + (n choose 2) + ... + (n choose n-1) + (n choose n)

so far my work is:
(n choose 0) = n!/0!n= 1
(n choose 1) = n
(n choose 2) = (-n)2/2!=1/2(n-1)n
(n choose n-1) = n!/1!(-1+n)! = n
(n choose n) = n!/0!n = 1
I don't know if I am approaching this the right way or how to approach this kind of question

thanks for any help!

(x+y)**n = Has the Expansion with the coeff.s you have provided that is


C(n,0)+C(n,1)+...+C(n,n-1)+C(n,n)

Set x=1;y=1;


(1+1)**n=2**n = Total of the coeff.s where we numerated x=y=1

Hope this Helps !