fiecare termen este :
1 - 1 /2 = ( 2 -1) /2 = 1 /2
1 - 1 /3 = (3 - 1) /3 = 2 /3
1 - 1 /4 = ( 4 - 1) /4 = 3 / 4
.........
1 - 1 /2000 = ( 2000 - 1) / 2000 = 1999 /2000
ex . = [1 /2] ² · [2 /3 ] ² · [ 3/4]² ······· [ 1998 / 1999 ]² · [1999 / 2000 ] ²
= 1 /4 · 4 /9 · 9/16 ······· 1998² / 1999² · 1999² /2000²
se simplifica numaratorii cu numitorii
ex = 1 / 2000² = [ 1 / 2000 ] ²