Câu hỏi của Sachiko

Question

S=1+2+2 mũ 2+...+2 mũ 9So sánh với 5.2 mũ 8

Minh Nguyễn Cao · Accepted Answer

$S=1+2+2^2+2^3+...+2^9$$2S=2+2^2+2^3+2^4+...+2^{10}$$2S-S=2-2+2^2-2^2+2^3-2^3+2^4-2^4+...+2^9-2^9+2^{10}-1$$S=2^{10}-1=2^8.2^2-1=2^8.4-1< 2^8.5$=> S < $2^8.5$Câu trả lời: $S=1+2+2^2+2^3+...+2^9$$2S=2+2^2+2^3+2^4+...+2^{10}$$2S-S=2-2+2^2-2^2+2^3-2^3+2^4-2^4+...+2^9-2^9+2^{10}-1$$S=2^{10}-1=2^8.2^2-1=2^8.4-1< 2^8.5$=> S < $2^8.5$

phạm thị kim yến · Answer

S= 1+$2^2$+$2^3$+...+$2^9$$\Rightarrow$2S=2+$2^2$+$2^3$+...+$2^{10}$$\Rightarrow$2S-S= (2+$2^2$+$2^3$+...+$2^{10}$)-(1+2+$2^2$+$2^3$+...$2^9$)$\Rightarrow$S= 2+$2^2$+$2^3$+...+$2^{10}$-1-2-$2^2$-$2^3$-...-$2^9$S=$2^{10}$-1ta có: (4+1) .$2^8$=4.$2^8$+$2^8$=$2^2$.$2^8$+$2^8$=$2^{10}$+$2^8$$\Rightarrow$$2^{10}$-1<$2^{10}$+$2^8$hay S<5.$2^8$Câu trả lời: S= 1+$2^2$+$2^3$+...+$2^9$$\Rightarrow$2S=2+$2^2$+$2^3$+...+$2^{10}$$\Rightarrow$2S-S= (2+$2^2$+$2^3$+...+$2^{10}$)-(1+2+$2^2$+$2^3$+...$2^9$)$\Rightarrow$S= 2+$2^2$+$2^3$+...+$2^{10}$-1-2-$2^2$-$2^3$-...-$2^9$S=$2^{10}$-1ta có: (4+1) .$2^8$=4.$2^8$+$2^8$=$2^2$.$2^8$+$2^8$=$2^{10}$+$2^8$$\Rightarrow$$2^{10}$-1<$2^{10}$+$2^8$hay S<5.$2^8$

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