Răspuns:
Explicație pas cu pas:
[tex]S=1+11+111+...+11..1=\dfrac{10-1}{9}+\dfrac{10^2-1}{9}+\dfrac{10^3-1}{9}+...+\dfrac{10^n-1}{9}= \dfrac{1}{9}*(10+10^2+10^3+...+10^n-n)[/tex]
10+10²+10³+...+10ⁿ este suma unei progresii geometrice cu primul termen b₁=10 si ratia q=10.
[tex]S_n=10*\dfrac{10^n-1}{10-1}=\dfrac{10^{n+1}-10}{9} \\Deci~S=\dfrac{1}{9}*( \dfrac{10^{n+1}-10}{9}-n)[/tex]
