Question

              tính nhanh :

    1 phần 4 +1 phần 8+ 1 phần 16+ 1 phần 32+ 1 phần 64

Answer 1

\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}.\)

\(A+\frac{1}{64}=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{64}\)

\(A+\frac{1}{64}=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{32}\)

\(A+\frac{1}{64}=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{16}=...=\frac{1}{2}\)

\(A=\frac{1}{2}-\frac{1}{64}=\frac{31}{64}.\)

Answer 2

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(=\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+\left(\frac{1}{8}-\frac{1}{16}\right)+\left(\frac{1}{16}-\frac{1}{32}\right)+\left(\frac{1}{32}-\frac{1}{64}\right)\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}\)

\(=\frac{1}{2}-\frac{1}{64}=\frac{31}{64}\)

Answer 3

31/64

Answer 4

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}=\frac{16}{64}+\frac{8}{64}+\frac{3}{64}+\frac{2}{64}+\frac{1}{64}=\frac{30}{64}=\frac{15}{32}\)