1/2 + 1/4 + 1/8+1/16=8/16+4/16+2/16+1/16=8+4+2+1/16=15/16
= 8/16 + 4/16 + 2/16 + 1/16
= 16/16
= 1
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(\Rightarrow A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\)
\(\Rightarrow2A=1+\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\right)\)
\(\Rightarrow A=1-\frac{1}{2^4}=1-\frac{1}{16}=\frac{15}{16}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
=\(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\)
=\(\frac{8+4+2+1}{16}=\frac{15}{16}\)
