P = (1 + 1/2) * (1 + 1/3) * (1 + 1/4) * ...............(1 + 1/99)
= (3/2) * (4/3) * (5/4) * (6/5) .................(100/99)
So here barring the denominator of the 1st term and the numerator of the last term , all other numbers will be cancelled out as they appear exactly once each in numerator and denominator..
= 100 / 2
= 50
Now
Q = (1 - 1/2) * (1 - 1/3) * (1 - 1/4) * .............. * (1 - 1/100)
= (1/2) * (2/3) * (3/4) * ............* (99/100)
Here barring numerator of first term and denominator of last term all others will be cancelled out..
= 1/100
Thus P/Q = 50/[1/100] = 5000