2+22+222+...+222...2 {de n ori} =
= 2·(1+11+111+...+111...1)
= 2·(9+99+999+...+999...9)/9
= 2·[(9+1)+(99+1)+(999+1)+...+(999...9+1)-1-1-...-1]/9
= 2·(10+100+1000+...+1000...0 - n)/9
= 2·(10+10²+10³+...+10ⁿ - n)/9
= 2·[10·(10ⁿ-1)/(10-1) - n]/9
= 2·[10·(10ⁿ-1)/9 - n]/9
