1) Prove, for all positive integers n , the identity
\frac{1}{n+1}+ \frac{1}{n+2} +... +\frac{1}{2n} =1- \frac{1}{2}+ \frac{1}{3}-...+ \frac{1}{2n-1} - \frac{1}{2n}.
2) The sequence x_{n} is given by x_{1} = 1 and x_{n+1} = \frac{4+ x_{n} }{1+ x_{n} } for n \geq 1.
a) Prove...