Question

Tìm E :

E=1+2+2^2+…….+2^2017

Answer 1

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

\(\Rightarrow2E=2\left(1+2+2^2+...+2^{2017}\right)\)

\(\Rightarrow2E=2+2^2+2^3+...+2^{2018}\)

\(\Rightarrow2E-E=2+2^2+2^3+...+2^{2018}-1-2-2^2-...-2^{2017}\)

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

Vậy \(E=2^{2018}-1\)

Answer 2

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

\(\Rightarrow2E=2+2^2+2^3+...+2^{2018}\)

\(\Rightarrow2E-E=(2+2^2+2^3+...+2^{2018}\text{)}-\left(1+2+2^2+...+2^{2017}\right)\)

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

Answer 3

E = 1 + 2 + 2² + ... + 2²⁰¹⁷
=> 2E = 2 + 2² + ... + 2²⁰¹⁷ + 2²⁰¹⁸
=> 2E - E = 2²⁰¹⁸ - 1
=> E = 22018 - 1
@Ogami rei