Two beautiful theorems

２つ の 新 の 数学 の法則 。。 過ぎ の 文章

Thm-1; Whats the sum of the coefficients in the expansion ..  ..

In  use x=1.

Then we have sum-of-all-coefficients =  .

Also total possible combinations of n things is .

 

Thm-2; In the above expansion the sum of odd coefficient is same as the sum of even coefficient. put x=-1, then from above;

1+∑even- coefficients = ∑odd-coefficients = 1/2(∑all-coefficients) =