+1836 (a) For what positive integers 
does 
have a nonzero constant term?
(b) For the values of that you found in part (a), what is that constant term? (You can leave your answer in the form of a combination.)
PLease explain very well
+129852 Amended answer...sorry, Mellie....I realized the answer I gave before was incorrect....
(a) It appears that a constant term will occur when n is a multiple of 3
For instance
When n = 3, the constant term is 3 = C(n, [2/3]n) = C(3,2)
When n = 6, the constant term is 15 = C(6,4)
When n = 9, the constant term is 84 = C(9,6)
(b) So ...it appears that the constant term is produced by C(n,[2/3]n)
This happens because at C(n, [2/3]n ).......x^1 is being raised to the [n - (2/3)n] = (1/3)n power...and...
x^-1 is being raised to the (2/3)n power....
So (x^2)^[(1/3)n] * (x^-1)^[(2/3)n] = (x)^(2/3)n * (x)^(-2/3)n = 1
And C(n, [2/3]n) * (1) = C(n, [2/3]n ) = a constant
+129852 Amended answer...sorry, Mellie....I realized the answer I gave before was incorrect....
(a) It appears that a constant term will occur when n is a multiple of 3
For instance
When n = 3, the constant term is 3 = C(n, [2/3]n) = C(3,2)
When n = 6, the constant term is 15 = C(6,4)
When n = 9, the constant term is 84 = C(9,6)
(b) So ...it appears that the constant term is produced by C(n,[2/3]n)
This happens because at C(n, [2/3]n ).......x^1 is being raised to the [n - (2/3)n] = (1/3)n power...and...
x^-1 is being raised to the (2/3)n power....
So (x^2)^[(1/3)n] * (x^-1)^[(2/3)n] = (x)^(2/3)n * (x)^(-2/3)n = 1
And C(n, [2/3]n) * (1) = C(n, [2/3]n ) = a constant
