Question

[๖ACE✪S̺͆E̺͆N̺͆O̺͆R̺͆I̺͆T̺͆A̺͆12★彡....]

Chứng minh rằng 2⁰ +2¹ +2² +...+2^5n-3 +2^5n-2 +2^5n-1  chia hết cho 31 nếu n là số nguyên dương bất kif

help me please

Answer 1

[Tran Le Khanh Linh]

Đặt A=\(2^0+2^1+2^2+....+2^{5n-3}+2^{5n-2}+2^{5n-1}\)

\(\Leftrightarrow A=\left(2^0+2^1+2^2+2^3+2^4+2^5\right)+...+\left(2^{5n+2}+2^{5n+1}+2^{5n}+2^{5n-1}+2^{5n-2}+2^{5n-3}\right)\)

\(\Leftrightarrow A=2^0\left(1+2+2^2+2^3+2^4\right)+....+2^{5n+2}\left(1+2+2^2+2^3+2^4\right)\)

\(\Leftrightarrow A=2^0\cdot31+2^5\cdot31+....+2^{5n+2}\cdot31\)

\(\Leftrightarrow A=31\cdot\left(2^0+2^5+...+2^{5n+2}\right)\)

\(\Rightarrow A⋮31\left(đpcm\right)\)

Answer 2

[๖ACE✪S̺͆E̺͆N̺͆O̺͆R̺͆I̺͆T̺͆A̺͆12★彡....]

quynh oi dpcm la gi vay?