Question

rút gọn biểu thức sau cho A = 1/2^1+1/2^2+1/2^3+....+1/2^99+1/2^100

tick ai nhanh đúng nhất

 

Answer 1

Ta có : \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+......+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)

\(\Leftrightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{99}}\)

=> 2A - A = 1 - \(\frac{1}{2^{100}}\)

<=> A = 1 - \(\frac{1}{2^{100}}\)

Answer 2

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

\(\Rightarrow2A=1+\frac{1}{2^1}+...+\frac{1}{2^{98}}+\frac{1}{2^{99}}\)

\(\Rightarrow2A-A=1-\frac{1}{2^{100}}\)

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