Question

cho C=1+4+4^2+4^3+4^5+4^6 tinh 4A và chung minh A= (4^7-1):3

 

 

Answer 1

\(4A=4+4^2+4^3+4^4+4^5+4^6+4^7\\ 4A-A=4^7-1\\ 3A=4^7-1\\ A=\dfrac{4^7-1}{3}44\)

Answer 2

ta có:\(A=1+4+...+4^6\Rightarrow4A=4+4^2+...+4^7\)

\(\)\(4A=4+4^2+..+4^7\\ \Rightarrow4A-A=\left(4+4^2+..+4^7\right)-\left(1+4+...+4^6\right)\\ \Rightarrow3A=4^7-1\\ \Rightarrow A=\dfrac{4^7-1}{3}\)

Answer 3

\(C=1+4+4^2+...+4^6\)

\(4C=4+4^2+...+4^7\)

\(4C-C=\left(4+4^2+...+4^7\right)-\left(1+4+4^2+...+4^6\right)\)

\(3C=4^7-1\)

\(\Rightarrow C=\dfrac{4^7-1}{3}\left(đpcm\right)\)