Question

So sánh :
  1 + 2 + \(2^2+2^3+......+2^{2009}\)và \(2^{2010}-1\)

Answer 1

Đặt A=1+2+2²+2³+...+2²⁰⁰⁹

      B=2²⁰¹⁰-1

=>2A=2+2²+2³+...+2²⁰¹⁰

=>2A-A=2²⁰¹⁰-1 hay A=2²⁰¹⁰-1=B
 

Answer 2

Đặt \(A=1+2+2^2+2^3+......+2^{2009}\)

\(2A=2+2^2+2^3+......+2^{2009}+2^{2010}\)

\(2A=2+2^2+2^3+......+2^{2009}+2^{2010}-\left(1+2+2^2+2^3+......+2^{2009}\right)\)

\(A=2^{2010}-1\)

Vậy \(1+2+2^2+2^3+......+2^{2009}=2^{2010}-1\)