Question

chứng tỏ rằng: \(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+...+\(\frac{1}{2^{100}}\)< 1

Answer 1

Đặt \(S=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)

\(\Rightarrow2S=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\)

\(\Rightarrow2S-S=1-\frac{1}{2^{100}}\)

\(\Rightarrow S=1-\frac{1}{2^{100}}< 1\) (đpcm)

Answer 2

trả lời giúp mình với!!!!

chiều mình thi