1÷(2÷3)÷(3÷4)÷(4÷5)÷(5÷6)······(2003÷2004)=?

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1÷(2÷3)÷(3÷4)÷(4÷5)÷(5÷6)······(2003÷2004)=?
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1÷(2÷3)÷(3÷4)÷(4÷5)÷(5÷6)······(2003÷2004)=?
1÷(2÷3)÷(3÷4)÷(4÷5)÷(5÷6)······(2003÷2004)=?

1÷(2÷3)÷(3÷4)÷(4÷5)÷(5÷6)······(2003÷2004)=?
=1×3/2×4/3×5/4×...×2003/2002×2004/2003=1/2×2004=1002

1÷(2/3)÷(3/4)÷(4/5)÷(5/6)÷······÷(2003/2004)
=1×3/2×4/3×5/4×6/5×······×2004/2003
=1/2×2004
=1002

1002