[tex]U(1)=1\\U(1\times2)=2\\U(1\times2\times3)=6\\U(1\times2\times3\times4)=U(24)=4\\U(1\times\boxed{2}\times3\times4\times\boxed{5})=0 \text{ because of } 2\times5=10\\U(1\times\boxed{2}\times3\times4\times\boxed{5}\times6)=0 \text{ because of } 2\times5=10\\....................\\....................\\U(1\times\boxed{2}\times3\times4\times\boxed{5}\times6\times...\times2019)=0 \text{ because of } 2\times5=10[/tex]
[tex]\implies~U(1+1\times2+1\times2\times3+1\times2\times3\times4+...+1\times2\times3\times....\times2019)=\\=U(1+1\times2+1\times2\times3+1\times2\times3\times4) = ~~~\text{(The others terms have U = 0)}\\=U(1+2+6+24)=U(33)=\boxed{\bf3}[/tex]
