Question

Tính nhanh

A=1/2+1/2²+1/2³+1/2⁴+...+1/2¹⁰

Giúp mình nhé

Answer 1

Ta có : 2A = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

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

A = \(1-\frac{1}{2^{10}}=\frac{1023}{1024}\)

Answer 2

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{1024}=\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{512}-\frac{1}{1024}\)

\(A=\frac{1}{2}-\frac{1}{1024}=\frac{511}{1024}\)