Question

S = \(\frac{1}{2}\) + \(\frac{1}{2^2}\) + \(\frac{1}{2^3}\) + ... + \(\frac{1}{2^{20}}\) < 1

Answer 1

Ta có: \(S=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\Rightarrow2S=1+\frac{1}{2}+...+\frac{1}{2^{19}}\)

\(2S-S=\left(1+\frac{1}{2}+...+\frac{1}{2^{19}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\right)\)

\(S=1-\frac{1}{2^{20}}\)

Vì \(1-\frac{1}{2^{20}}

Answer 2

Ghi sai đề rồi : Phải là \(CMR:S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{20}}

Answer 3

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