Question

Cho S = 1+2+2²+2³+........+2⁹

^{Tinh tong S} 

So sanh voi P = 5.2⁸       Minh  cam on

 

Answer 1

\(S=1+2+2^2+2^3+...+2^9\)

\(2S=2+2^2+2^3+2^4+...+2^{10}\)

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

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

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

\(P=4.\frac{5}{4}.2^8\)

\(P=2^2.2^8.\frac{5}{4}=2^{10}.\frac{5}{4}\)

\(\Rightarrow S< P\)

Answer 2

S < P nhe

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Answer 3

S = 1 + 2 + 2^2 + 2^3 + ... + 2 ^ 9 . 

S = 2^10 - 1 .