Đáp án:
$\begin{array}{l}
a = 5 + {5^2} + {5^3} + ... + {5^{2010}}\\
= \left( {5 + {5^2}} \right) + \left( {{5^3} + {5^4}} \right) + ... + \left( {{5^{2009}} + {5^{2010}}} \right)\\
= 5\left( {1 + 5} \right) + {5^3}\left( {1 + 5} \right) + ... + {5^{2009}}\left( {1 + 5} \right)\\
= 5.6 + {5^3}.6 + .. + {5^{2009}}.6\\
= 6\left( {5 + {5^3} + .. + {5^{2009}}} \right) \vdots 6\\
\Rightarrow a \vdots 6\\
b)co:a \vdots 5;\,a \vdots 6 \Rightarrow a \vdots 5.6 \Rightarrow a \vdots 30\\
\Rightarrow a\,chia\,cho\,31\,du\,30.\\
c){5^{1\,}},{5^2},...,{5^{2010}}\,\,\tan \,cung\,la\,5\\
\Rightarrow tổng\,a\,gồm\,2010\,số\,hạng\,có\,\tận \,cùng\,là\,0
\end{array}$
