Question

Calculați suma : 9+99+999+...+{99...9} de 1998 ori 9

Repede vă rooog !! Până la ora 15:00 ! Dau 15 puncte !!

Answer 1

9+99+999+...+999...9 {de 1998 ori} =

= (10-1)+(100-1)+(1000-1)+....+(1000...0-1) {de 1998 ori}

= 10+100+1000+...+1000...0 - 1998

= 10¹ + 10² + 10³ + ... + 10¹⁹⁹⁸ - 1998

= 10·(10¹⁹⁹⁸ - 1)/(10-9) - 1998

= (10¹⁹⁹⁹ - 1)/9 - 1998

= (10¹⁹⁹⁹ - 17983)/9