Câu hỏi của Nguyễn Vũ Linh Nhi

Question

So sánh A=2⁰+2¹+2²+....+2²⁰¹⁰ và B=2²⁰¹¹-1

Nguyễn Như Ý · Accepted Answer

$A=2^0+2^1+2^2+...+2^{2010}$

=>$2A=2^1+2^2+2^3+...+2^{2011}$

=> $2A-A=\left(2^1+2^2+2^3+...+2^{2011}\right)-\left(2^0+2^1+2^2+...+2^{2010}\right)$

=> $A=2^{2011}-2^0=2^{2011}-1=B$

Câu trả lời:

$A=2^0+2^1+2^2+...+2^{2010}$

=>$2A=2^1+2^2+2^3+...+2^{2011}$

=> $2A-A=\left(2^1+2^2+2^3+...+2^{2011}\right)-\left(2^0+2^1+2^2+...+2^{2010}\right)$

=> $A=2^{2011}-2^0=2^{2011}-1=B$