Thread: recurrence problem...

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

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

u're absolutely right
sorry that i did'nt type the question correctly.

anyway,
thanx a lot!!