Question

cho S = 1+2+2mũ 2+2mũ 3+.....+2 mũ 9

Hãy so sánh S với 5 nhân 2mũ 8

Answer 1

\(S=1+2+2^2+...+2^9\)

\(\Rightarrow2S=2+2^2+2^3+...+2^{10}\)

\(\Rightarrow S=2^{10}-1\)

Lại có \(5.2^8=\left(2^2+1\right).2^8=2^{10}+2^8\)

Vậy \(S< 5.2^8\)

Answer 2

S=1+2+2^2+2^3+...+2^9​

2S=2+2^2+2^3+...+2^9+2^10

2S-S=(2+2^2+2^3+...+2^9+2^10)-(1+2+2^2+2^3+...+2^9)

S=2^10-1

5.2^8=(2^2+1).2^8=(2^2.2^8)+(1.2^8)=2^10+2^8

Vì 2^10-1<2^10+2^8=> S<5.2^8

Vậy S < 5. 2^8

Answer 3

Ta có: \(S=1+2+2^2+2^3+...+2^9\)

\(\Rightarrow2S=2+2^2+2^3+...+2^{10}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+...+2^{10}\right)-\left(1+2+2^2+...+2^9\right)\)

\(\Rightarrow S=2^{10}-1\)

Mặt khác: \(5.2^8=\left(1+2^2\right).2^8=2^8+2^2.2^8=2^8+2^{10}\)

Vì \(2^{10}-1< 2^8+2^{10}\Rightarrow S< 5.2^8\)

Answer 4

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