Question

S=1+2+2²+2³+...+2⁹. So sánh S với 5. 2⁸

 

Answer 1

$S=1+2+2^2+...+2^9$

$2S=2\left(1+2+2^2+...+2^{10}\right)$

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

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

\(S=2^{10}-1=2^2.2^8-1=4.2^8-1

 

HT

Answer 2

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

\(S=\dfrac{2^{9+1}-1}{2-1}\)

\(S=2^{10}-1=1023\)

\(5.2^8=5.256=1280>1023\)

\(\Rightarrow S< 5.2^8\)

Answer 3

S < 5. 2^8

Answer 4

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

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

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

\(S=-1+2^{10}\)hay \(2^{10}-1=1023\)

Mà \(5\cdot2^8=1280\)

Nên \(2^{10}-1< 5\cdot2^8\)

Vậy \(S< 5\cdot2^8\)

Answer 5

$S=1+2+2^2+...+2^9$

$2S=2\left(1+2+2^2+...+2^{10}\right)$

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

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

\(S=2^{10}-1=2^2.2^8-1=4.2^8-1