Question

calculati suma cifrelor numarului A , unde : A=9+ 99+ 999+....+9999999999

Answer 1

......................................

Answer 2

$\it A = (10-1) +(10^2-1) +(10^3-1) +\ ...\ + (10^{10-1}) = \\ \\ = 10^{10} +10^9 +\ ...\ +10^2+10-10 = 10^{10} +10^9 +\ ...\ +10^2 = \\ \\ = \underbrace{111\ ...\ 1}_{9cifre} 00$

Suma cifrelor numărului A este :

$\ S = \underbrace{1+1+1+\ ...\ +1}_{de \ 9\ ori} =9$