i) I think the recurrence is not true.
Then
ii)
Every factor of the product is greater then 1, so the entire factor is greater than 1. Therefore
do u have any idea on this?
question :
let n >=2, 0 < X1< X2 <....< Xn-1 < Xn,
for Xk , k=1,2,....,n to be integers
Define
Sn=(1 + 1/X1)(1 + 1/X2)....(1 + 1/Xn) - 1,
then
i) Show the recurrence Sn-1 = Xn/(Xn+1) Sn - 1
ii)If Sn and Sn-1 are positive integers then Sk is also a positive integer for every k=1,2,3,.....,n