$$
4 \cdot 55 \text { when } 1-x>(1-x)^{2}>(1-x)^{3}
$$
$>(1-x)^{4}>\cdots$ , the range of $x$ is
(A) $x>1$.
(B) $x0$.
(D) $x<0$.
(E) $0<x<1$.
(China Hubei Province Wuhan City Junior High School Mathematics Competition, 1985)
[Solution] From $1-x>(1-x)^{2}$, we get $0<x<1$. When $0<x<1$, $0<1-x<1$. Therefore, the inequalities in the question all hold. Hence, the answer is $(E)$.