9+99+999+9999+99999+...+9999...99 {de 2019 ori} =
= 10+100+1000+10000+100000+...+10000...00 {de 2019 ori} -
- 1-1-1-1-...-1 {de 2019 ori}
= 10+10²+10³+10⁴+...+10²⁰¹⁹ - 1·2019
= 10·(10²⁰¹⁹-1)/(10-1) - 2019
(Am aplicat formula sumei de progresie geometrică.)
= (10²⁰²⁰ - 10)/9 - 2019
= (10²⁰²⁰ - 18181)/9
