O sa fac suma fara radical mai intai:
[tex]S = 6 + 5(6^{1}+6^{2}+6^{3}+...+6^{2010})\\
S_{1}=6^{1}+6^{2}+6^{3}+...+6^{2010}[/tex]
Inmultim S1 cu 6:
[tex]6S_{1}=6^{2}+6^{3}+6^{4}+...+6^{2010}+6^{2011}\\
6S_{1}=S_{1}-6^{1}+6^{2011}\\
5S_{1}=6^{2011}-6\\
S_{1}= \frac{6^{2011}-6}{5} \\\\
S=6+5S_{1}=6+6^{2011}-6=6^{2011}[/tex]
[tex] \sqrt{S}= \sqrt{6^{2011}} = \sqrt{36^{ \frac{2011}{2} }} = 36^{ \frac{2011}{4} } \rightarrow \frac{2011}{4}=101x\\
x= \frac{2011}{404} [/tex]
