SOLUTION: Please show the following: (1+2nC1 + 2nC2 +2nC3 +...+ 2nC(2n-1) + 2nC2n)^2 = 16^n.

Algebra ->  Permutations -> SOLUTION: Please show the following: (1+2nC1 + 2nC2 +2nC3 +...+ 2nC(2n-1) + 2nC2n)^2 = 16^n.      Log On


   

Question 1045495: Please show the following:
(1+2nC1 + 2nC2 +2nC3 +...+ 2nC(2n-1) + 2nC2n)^2 = 16^n.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
It is enough to show that
+...+ %28matrix%282%2C1%2C2n%2C2n%29%29+=+4%5En. (Why?)

It is known that +...+ %28matrix%282%2C1%2C2n%2C2n%29%29%2Ax%5E%282n%29.
Letting x = 1, get directly
+...+ %28matrix%282%2C1%2C2n%2C2n%29%29.
And that's it...