Let
     1      1             1   
P = --- + ---- + .....+ ------
    1*2    3*4          99*100
    
      1        1             1
Q = ------ + ------ + ....+ ------
    51*100   52*99          100*51

Express P/Q in its lowest terms, that is, gcd(P,Q)=1

*** Adapted from a problem appearing at Argentina Mathematical Olympiad in 2014