Question

[Nhã Uyên]

giúp minh cau nay vs nhé

A= 75. (4^2004 + 4^2003 +...+4^2 +4+1)+25 là số chia hết cho 100

Answer 1

[Isolde Moria]

\(A=75\left(4^{2004}+4^{2003}+....+4+1\right)+25\)

\(\Rightarrow A=75.4^{2004}+75.4^{2003}+....+75.4+75.1+25\)

\(\Rightarrow A=\left(75.4\right).4^{2003}+....+300+100\)

\(\Rightarrow A=300.4^{2003}+.....+300+100\) chia hết cho 100

=> ĐPCM

Answer 2

[Lê Việt Anh]

B=4^2004+4^2003+...+4^2+4+1
Xét 4B = 4^2005+4^2004+...+4^2+4
=> 4B-B = (4^2005+4^2004+...4^3+4^2+4) - (4^2004+4^2003+...+4^2+4+1)
=> 3B = 4^2005 - 1 => B = (4^2005 - 1)/3
=> A = 75 (4^2005 - 1)/3 +25
= 25 (4^2005 -1) +25
= 25 x 4 ^ 2005
= 25 x 4 x 4 ^ 2004 = 100 x4 ^ 2004