Question

So sanh A va b

A=1+2+2²+2³+...+2²⁰¹⁰

B=2²⁰¹¹-1

Answer 1

\(A=1+2+2^2+2^3+...+2^{2010}\)

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

\(2A=2+2^2+2^3+2^4+...+2^{2011}\)

\(A=2A-A=\left(2+2^2+2^3+2^4+..+2^{2011}\right)-\left(1+2+2^2+2^3+..+2^{2010}\right)\)

\(A=2^{2011}-1\)

Vì \(A=2^{2011}-1;B=2^{2011}-1\Rightarrow A=B\)

Answer 2

A= 1+2+2²+2³+...+2²⁰¹⁰

2A=2 (2+2²+2³+...+2²⁰¹⁰)

2A=2²+2³+2⁴+...+2²⁰¹¹

2A-A= 2²⁰¹¹-1

A= 2^2011-1

Ta có: 2²⁰¹¹-1=2²⁰¹¹-1

\(\Rightarrow\)...=...Còn lại