Show that for natural numbers x and y if x/y > 1 then
x
y
 > (x+1)
(y+1)
 > 1.
Hence prove that
P = 2
1
 . 4
3
 . 6
5
 ... k
k-1
 >   ___
Ök+1
 
 .
This shows that the product
P=Pi=1n 2i
2i-1

tends to infinity as n tends to infinity. Now, using a similar method, show that
Q = 2
1
 . 4
3
 . 6
5
 ... 100
99
 > 12.