Question

Ofer 15 puncte!!! Ce trebuie sa fac in continuare la exercițiu? ​

Answer 1

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