Question

afla numarul N stind ca N= 2+22+222+2222+.......+22222222

Answer 1

N = 2+22+222+2222+...+222...2

N/2 = 1+11+111+1111+...+111...1

9N/2 = 9+99+999+9999+...+999...9

9N/2 + (1+1+1+1+....+1) =

= 10+100+1000+10000+...+1000...0

9N/2 + 8 = 10+10²+10³+10⁴+...+10⁸

9N/2 + 8 = 10•(10⁸-1)/(10-1)

9N/2 + 8 = (10⁹ - 10)/9

81N/2 + 72 = 10⁹ - 10

81N/2 = 10⁹- 82

81N = 2•(10⁹ - 82)

N = 2•(10⁹ - 82)/81