Question

 Tính: 

A= 1+2+2^2+...2^2008/1-2^2009

Answer 1

Xét tử số

M=1+2+2²+...+2²⁰⁰⁸ 

2M=2+2²+2³+...+2²⁰⁰⁹

M = 2²⁰⁰⁹-1

=> A=\(\frac{2^{2009}-1}{1-2^{2009}}=-1\)

Answer 2

Ta có: \(A=\frac{1+2+2^2+...+2^{2008}}{1-2^{2009}}\)

Đặt B = 1 + 2 + 2² + ... + 2²⁰⁰⁸

=> 2B = 2 + 2² + 2³ + ... + 2²⁰⁰⁹

=> 2B - B = (2 +2² + 2³ +...+ 2²⁰⁰⁹) - (1 + 2 + 2² + ...+2²⁰⁰⁸)

=> B = 2²⁰⁰⁹ - 1

\(\Rightarrow A=\frac{2^{2009}-1}{1-2^{2009}}=\frac{-1-2^{2009}}{1-2^{2009}}=-1\)

Vậy A = -1