Cho \[M = 2 + {2^2} + {2^3} + \ldots + {2^{20}}.\] Chứng tỏ rằng \[M\;\,\, \vdots \,\,5\]

\(\begin{array}{l}2 + {2^2} + {2^3} + {2^4} + .... + {2^{20}}\\ = (2 + {2^2} + {2^3} + {2^4}) + ... + ({2^{17}} + {2^{18}} + {2^{19}} + {2^{20}})\\ = (2 + {2^2} + {2^3} + {2^4}) + ... + {2^{16}}(2 + {2^2} + {2^3} + {2^4})\\ = 30.1 + ... + {2^{16}}.30 = 30.(1 + ... + {2^{16}}) \vdots 5\end{array}\)