Question

Cho A=1+2^1+2^1+2^2+2^3+...+2^2007

a)Tính 2A

b)Chứng Minh:A=2^2008-1

Answer 1

sửa đề: A=1+2+2^2+...+2^2007

a: \(2\cdot A=2+2^2+2^3+...+2^{2008}\)

b: \(2\cdot A=2^{2008}+2^{2007}+...+2^3+2^2+2\)

\(A=2^{2007}+2^{2006}+...+2+1\)

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

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

Answer 2

a) 2A = 2 + 2² + 2³ +...+ 2²⁰⁰⁸

b) ......................... =) A = 2²⁰⁰⁸ - 1

Answer 3

Sửa đề:\(1+2+2^2+...+2^{2007}\)

a) \(2A-A=2.\left(1+2+2^2+...+2^{2007}\right)-\left(1+2+2^2+...+2^{2007}\right)\)

b) \(2A-A=2.\left(1+2+2^2+...+2^{2007}\right)-\left(1+2+2^2+...+2^{2007}\right)\)

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

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