Câu hỏi của Nguyen The Anh

Question

Cho A = 1+2+22+22+5……… +298+299 so sánh A với 5×298

Lê Minh Anh · Accepted Answer

$A=1+2+2^2+2^3+2^4+.....+2^{98}+2^{99}$$\Rightarrow2A=2+2^2+2^3+2^4+2^5+.....+2^{99}+2^{100}$$\Rightarrow2A-A=\left(2+2^2+2^3+2^4+.....+2^{99}+2^{100}\right)-\left(1+2+2^2+2^3+.....+2^{98}+2^{99}\right)$$\Rightarrow A=2^{100}-1=2^{98}\times2^2-1=2^{98}\times4-1< 2^{98}\times5$Vậy A < 298 x 5Câu trả lời: $A=1+2+2^2+2^3+2^4+.....+2^{98}+2^{99}$$\Rightarrow2A=2+2^2+2^3+2^4+2^5+.....+2^{99}+2^{100}$$\Rightarrow2A-A=\left(2+2^2+2^3+2^4+.....+2^{99}+2^{100}\right)-\left(1+2+2^2+2^3+.....+2^{98}+2^{99}\right)$$\Rightarrow A=2^{100}-1=2^{98}\times2^2-1=2^{98}\times4-1< 2^{98}\times5$Vậy A < 298 x 5

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