Question

9+99+999+... + 999..... 99 de 100 de ori Câte cifre de 1 conţine nr ?​Va rog e fffffff urgentttttttt

Answer 1

Explicație pas cu pas:

$9 + 99 + 999 + ... + \underbrace{999...99}_{100} =$

$= (10-1) + (100-1) + (1000-1) + ... + (1\underbrace{000...00}_{100}-1)$

$= 10 + \red { \bf100} + 1000 + ... + 1\underbrace{000...00}_{100} - \red { \bf100}$

$= 10 + 1000 + ... + 1\underbrace{000...00}_{100}$

$= \underbrace{111...111}_{98}010$

=> sunt 99 cifre de 1