U_{n+1}=1/U_{n} where U_{1}= 2/3First of all, we need to find U_{2} and U_{3} and so on, up until we notice a pattern in the answers. U_{2} = 1/(2/3) = 3/2U_{3} = 1/(3/2) = 2/3As we can see, U_{1} and U_{3} are equal, and so we know that for every 'n' that is odd, U_{n} will equal 2/3. This is similar for ever 'n' that even where U_{n} will equal 3/2.Therefore in total for this summation, there will be 50 lots of '2/3' and 50 lots of '3/2' so the answer will be 50(2/3) + 50(3/2) = 325/3