Hi my name is Anna and I'm a senior in college. I am a student.

Question: how can I prove that 2nCn is less than 4^{n}, for all positive integers n? Any help would be greatly appreciated.

Anna,

One way is use the binomial theorem to expand (1+x)^{2n} and note that one of the terms is 2nCnx^{n}; now what happens if you set x = 1?

Penny