巧算:1÷(1+1/2)÷(1+1/3)÷(1+1/4)÷……÷(1+1/20)=1÷(1+1/2)÷(1+1/3)÷(1+1/4)÷……÷(1+1/20)=

问题描述:

巧算:1÷(1+1/2)÷(1+1/3)÷(1+1/4)÷……÷(1+1/20)=
1÷(1+1/2)÷(1+1/3)÷(1+1/4)÷……÷(1+1/20)=

=1÷(3/2)÷(4/3)÷(5/4)÷(6/5)……÷(21/20)
=1×(2/3)×(3/4)×(4/5)……×(19/20)×(20/21)
=2/21