Question

[Thu Thủy Nguyễn]

Cho A = 1+2¹+2²+2³3+...+2²⁰⁰⁷

a)Tính 3A

b)Chứng minh : A = 2²⁰⁰⁸--1

Answer 1

[Minh Hiếu]

A \(=\)\(1+2^1+2^2+...+2^{2007}\)

⇒2 A \(=\)\(2+2^2+...+2^{2007}+2^{2008}\)

2A - A \(=\)( \(2+2^2+...+2^{2007}+2^{2008}\) ) - ( \(1+2^1+2^2+...+2^{2007}\) )

A\(=\)\(2^{2008}-1\)

\(3A=3\left(2^{2008}-1\right)\)

      \(=3.2^{2008}-3\)