Question

Tính \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\)

Answer 1

nhớ có lời giải nha mấy bạn

Answer 2

\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}=\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+\frac{1}{2.2.2.2}=\frac{1.2.2.2}{2.2.2.2}+\frac{1.2.2}{2.2.2.2}+\frac{1.2}{2.2.2.2}+\frac{1}{2.2.2.2}\)

\(=\frac{8+2+2+1}{16}=\frac{13}{16}\)

Answer 3

\(A=\frac{1}{2}+^{^{^{ }}}\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}\)

\(2A-A=1-\frac{1}{2^4}\)

\(A=1-\frac{1}{16}=\frac{15}{16}\)