Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\left( {2n - 3} \right)\,\, \vdots \,\,\left( {n + 1} \right)\\
\Leftrightarrow \left[ {\left( {2n + 2} \right) - 5} \right]\,\, \vdots \,\,\left( {n + 1} \right)\\
\Leftrightarrow \left[ {2.\left( {n + 1} \right) - 5} \right]\,\, \vdots \,\,\left( {n + 1} \right)\\
2.\left( {n + 1} \right)\,\, \vdots \,\,\left( {n + 1} \right)\\
\Rightarrow 5\,\, \vdots \,\,\left( {n + 1} \right)\\
\Rightarrow \left( {n + 1} \right) \in Ư\left( 5 \right) = \left\{ {1;5} \right\}\\
\Rightarrow n \in \left\{ {0;4} \right\}\\
b,\\
\left( {3n + 5} \right)\,\, \vdots \,\,n\\
3n\,\, \vdots \,\,n \Rightarrow 5\,\, \vdots \,\,n\\
\Rightarrow n \in Ư\left( 5 \right) = \left\{ {1;5} \right\}\\
c,\\
A = 1 + 5 + {5^2} + {5^3} + ..... + {5^{204}} + {5^{205}} + {5^{206}}\\
= \left( {1 + 5 + {5^2}} \right) + \left( {{5^3} + {5^4} + {5^5}} \right) + ...... + \left( {{5^{204}} + {5^{205}} + {5^{206}}} \right)\\
= \left( {1 + 5 + {5^2}} \right) + {5^3}.\left( {1 + 5 + {5^2}} \right) + ..... + {5^{204}}.\left( {1 + 5 + {5^2}} \right)\\
= 31 + {5^3}.31 + ..... + {5^{204}}.31\\
= 31.\left( {1 + {5^3} + ..... + {5^{204}}} \right)\,\, \vdots \,\,31
\end{array}\)
