Câu hỏi của Nguyễn Hiền

Question

Rút gọn:A= 2+23+25+...+22009

Nguyễn Ngọc An · Accepted Answer

$A=2+2^3+2^5+...+2^{2009}$$\Rightarrow2^2A=2^2\left(2+2^3+2^5+...+2^{2009}\right)$$\Rightarrow2^2A=2^3+2^5+2^7...+2^{2011}$$\Rightarrow2A-A=\left(2^3+2^5+2^7...+2^{2011}\right)-\left(2+2^3+2^5+...+2^{2009}\right)$$\Rightarrow2A-A=2^3+2^5+2^7...+2^{2011}-2-2^3-2^5-...-2^{2009}$$\Rightarrow A=2^{2011}-2$Câu trả lời: $A=2+2^3+2^5+...+2^{2009}$$\Rightarrow2^2A=2^2\left(2+2^3+2^5+...+2^{2009}\right)$$\Rightarrow2^2A=2^3+2^5+2^7...+2^{2011}$$\Rightarrow2A-A=\left(2^3+2^5+2^7...+2^{2011}\right)-\left(2+2^3+2^5+...+2^{2009}\right)$$\Rightarrow2A-A=2^3+2^5+2^7...+2^{2011}-2-2^3-2^5-...-2^{2009}$$\Rightarrow A=2^{2011}-2$

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