[tex]( \frac{5}{7}+ \frac{5*11}{7*11}+ \frac{5*111}{7*111}]: \frac{5}{7}=(\frac{5}{7}+ \frac{5}{7}+ \frac{5}{7}): \frac{5}{7} = \\ \\ = \frac{15}{7}* \frac{7}{5}=3 \\ \\ \frac{111}{500}:( \frac{1}{5}+ \frac{1}{50}+ \frac{1}{500}) \frac{111}{500}: \frac{111}{500} = \\ \\= \frac{111}{500}* \frac{500}{111} =1 \\ \\ =( {\frac{ \frac{1}{11}+ \frac{1}{101}+..... \frac{1}{1000...01}}{\frac{1}{55}+ \frac{1}{505}+..... \frac{1}{5000...05}}}^})}^{n+1}\\ \\[/tex]
prima parte devine
(3-1)ⁿ=2ⁿ
cea mai complicata se reduce tot caci la numitor dam factor comun 1/5
si devine
[tex] 5^{n+1} [/tex]
[tex] 2^{n}*[/tex][tex] 5^{n+1} [/tex]=2*5²
