Toán Lớp 6: Cho A = 1 + 2 + 2 ² + 2 ³ + 2 mũ 2004 chia hết 31

Question

Toán Lớp 6:  Cho A = 1 + 2 + 2 ² + 2  ³ + 2  mũ 2004 chia hết 31

mytamhoang · Answer

A=2+2^2+2^3+......+2^{2004}   A=(2+2^2+2^3+2^4+2^5)+......+(2^{2000}+2^{2001}+2^{2002}+2^{2003}+2^{2004})   A=2.(1+2+2^2+2^3+2^4)+.....+2^{2000}.(1+2+2^2+2^3+2^4)   A=2.31+.....+2^{2000}.31   A=31.(2+....+2^{2000})    $ text{V&igrave;}$ 31 $ vdots$ 31 $ Rightarrow$ 2+....+2^{2000} $ vdots$ 31   $ Rightarrow$ 31.(2+....+2^{2000}) $ vdots$ 31   $ text{Vậy A}$ $ vdots$ 31

annhocbichchaubich · Answer

$  $   Sửa đề :   A = 2+2^2+...+2^{2003}+2^{2004}   ->A=(2+2^2+2^3+2^4+2^5)+...+(2^{2000}+2^{2001}+2^{2002}+2^{2003}+2^{2004})   ->A = (2 . 1 + 2 . 2 +2 . 2^2 + 2 . 2^3 + 2 . 2^4)+...+(2^{2000} . 1 +2^{2000} . 2 +2^{2000}.2^2 +2^{2000} . 2^3+2^{2000} . 2^4)   -> A = 2 . (1+2+2^2 +2^3 +2^4)+...+2^{2000} . (1+2+2^2+2^3+2^4)   -> A = 2 . (1+2+4+8+16) + ... + 2^{2000} . (1+2+4+8+16)   ->A=2 . 31 + ... + 2^{2000} . 31   ->A = 31 . (2+...+2^{2000})   V&igrave; 31 chia hết cho 31   ->31 . (2+...+2^{2000}) chia hết cho 31   -> A chia hết cho 31 (đpcm)