Find the term independent of x in the expansion of

Question

100
4
3
2





x
x

Answer 1

The given expression is:

(1 - x/4)^100

Using the binomial theorem, we can expand this as:

∑(100 choose k)*(1)^(100-k)*(-x/4)^k

= ∑(100 choose k)*(-1)^k*(x/4)^k

The term independent of x corresponds to k = 0, since any power of x greater than 0 will have a factor of x. Therefore, the term independent of x is:

(100 choose 0)*(-1)^0*(1/4)^0 = 1.

So the answer is 1.