mathematical analysis problem. please help.

suppose {x(n)} is a sequence such that

x(1)=1 and

x(n+1)=1+x(n)/(1+x(n+1)) ; n>=1

Prove that this sequence converges and find the limit.

I know how to find the limit of this sequence but dont know how to show that {x(n)} is a convergent sequence. Please help me on this.

oops i had a typo in the question.

here is the correct problem. In the original question i had 1+x(n)/(1+x(n+1)) but it should be 1+x(n)/(1+x(n)).

suppose {x(n)} is a sequence such that

x(1)=1 and

x(n+1)=1+x(n)/(1+x(n)) ; n>=1

Prove that this sequence converges and find the limit.

I know how to find the limit of this sequence but dont know how to show that {x(n)} is a convergent sequence. Please help me on this.