Seeking help from an exercise of binomial theorem in Senior High School (1+x)^3+(1+x)^4+… +In the expansion of (1 + x) ^ 2004, the coefficient of x ^ 3 is equal to () A.C2004 4 B.C2005 4 C.2C2004 3 D.2C2005 3 Note: c2004 4 is the combination number, 2004 in the bottom, 4 in the top

Seeking help from an exercise of binomial theorem in Senior High School (1+x)^3+(1+x)^4+… +In the expansion of (1 + x) ^ 2004, the coefficient of x ^ 3 is equal to () A.C2004 4 B.C2005 4 C.2C2004 3 D.2C2005 3 Note: c2004 4 is the combination number, 2004 in the bottom, 4 in the top

B

A problem of binomial theorem
The constant term of {x ^ (1 / 3) - 1 / [x ^ (1 / 2)]} ^ 15 expansion is?
Let's put it in words again. The constant term expanded to the 15th power of (the third root of x) minus (the second root of x) is?

6
{x^（1/3）-1/[x^(1/2)]}^15=x^(1/2){x^(1/6)-1}^15
The constant term in the expansion is the 13th term
x^(1/2)*(15-12)*(15-13)*(15-14)*x^[(15-12)/6]*(-1)^12
=6x^[3/6]*x^(1/2)=6

A problem about binomial theorem
In the expansion of (1 + 2x) n, the coefficients of the sixth term and the seventh term are equal, and the term with the largest coefficient in the expansion is obtained

T6 = C (n, 5) *