Groups and the Group Axioms · Superchallenge problem

On the interval $(-1,1)$ define $a*b=\dfrac{a+b}{1+ab}$. This operation makes $(-1,1)$ a group with identity $0$. Find the value of $\tfrac{1}{2}*\tfrac{1}{3}*\tfrac{1}{4}*\cdots*\tfrac{1}{10}$.