In the 100th expansion of (1 + x-k * x), find the value of K which makes the coefficient of the 4th term of x the minimum

In the 100th expansion of (1 + x-k * x), find the value of K which makes the coefficient of the 4th term of x the minimum

The coefficient of the fourth term is as follows
C(100,4)-kC(100,1)*C(99,2) +k ^2*C(100,2),
This is a quadratic expression of K, and the axis of symmetry is
{C(100,1)*C(99,2)}/2*C(100,2)=49,
So when k = 49, the coefficient of the fourth power term is the minimum
Note: C (100,4) is the combination of 4 out of 100, and all of the 100 factors take x terms,
KC (100,1) * C (99,2) means that there is a factor taking the square term of X, and then two terms of X are taken from the remaining 99 terms,
K ^ 2 * C (100,2), i.e. take the square of two terms x from 100 terms