Question

Cho A=1+2+2^2+2^3+...+2^2017. Chứng minh rằng A=2^2018 -1.

Answer 1

\(A=1+2+2^2+2^3+...+2^{2017}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2018}\right)-\left(1+2+2^2+...+2^{2017}\right)\)

\(\Rightarrow A=2^{2018}-1\left(đpcm\right)\)

Answer 2

\(A=1+2+2^2+2^3+...+2^{2017}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2018}\right)\)\(-\left(1+2+2^2+...+2^{2017}\right)\)

\(\Rightarrow A=2^{2018}-1\)

Answer 3

A=1+2+2^2+2^3+...+2^2017

2A=2+2^2+2^3+2^4+...2^2018

=> A= 2A - A = 2+2^2+2^3+2^4+...+2^2018-1+2+2^2+2^3+...+2^2017

=>A=2^2018-1

hok tốt!