Question

Tính 1/2 + 1/4 + 1/8 + 1/16 + 1/32

Answer 1

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow\)\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)

\(\Rightarrow\)\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)

\(\Leftrightarrow\)\(A=1-\frac{1}{32}=\frac{31}{32}\)

Answer 2

Đặt \(K=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow2K=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)

\(\Rightarrow2K-K\)

\(=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)

\(=1-\frac{1}{32}=\frac{31}{32}\)

Vậy \(K=\frac{31}{32}\)

Answer 3

đặt \(A=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{32}\)

\(\Rightarrow2A=1+\frac{1}{2}+...+\frac{1}{16}\)

\(\Rightarrow2A-A=(1+\frac{1}{2}+...+\frac{1}{16})-(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{32})\)

\(\Rightarrow A=1-\frac{1}{32}\)

\(\Rightarrow A=\frac{31}{32}\)

Answer 4

= \(\frac{31}{32}\)