$(1-\frac{1}{1931}).(1-\frac{1}{1932}).(1-\frac{1}{1933}).(1-\frac{1}{1934})........(1-\frac{1}{2019})$
$=\frac{1931-1}{1931}.\frac{1932-1}{1932}.\frac{1933-1}{1933}. ... .\frac{2019-1}{2019}$
$=\frac{1930}{1931}.\frac{1931}{1932}. ... .\frac{2018}{2019}$
$=\frac{1930}{2019}$