Đáp án: \(\frac{{511}}{{510}}\)

Hướng dẫn:

\(A = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... + \frac{1}{{512}}\)

\(A \times 2 = 1 + \frac{1}{2} + \frac{1}{4} + ... + \frac{1}{{256}}\)

\(A \times 2 - A = 1 - \frac{1}{{512}}\)

\(A = \frac{{511}}{{512}}\)

\(B = \frac{1}{{1 + 2}} + \frac{1}{{1 + 2 + 3}} + \frac{1}{{1 + 2 + 3 + 4}} + ... + \frac{1}{{1 + 2 + 3 + ... + 511}}\)

\(B = \frac{1}{{\left( {1 + 2} \right) \times 2:2}} + \frac{1}{{\left( {1 + 3} \right) \times 3:2}} + \frac{1}{{\left( {1 + 4} \right) \times 4:2}} + ... + \frac{1}{{\left( {1 + 511} \right) \times 511:2}}\)

\(B = \frac{1}{{2 \times 3:2}} + \frac{1}{{3 \times 4:2}} + \frac{1}{{4 \times 5:2}} + ... + \frac{1}{{511 \times 512:2}}\)

\(B \times \frac{1}{2} = \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + ... + \frac{1}{{511 \times 512}}\)

\(B \times \frac{1}{2} = \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + ... + \frac{1}{{511}} - \frac{1}{{512}}\)

\(B \times \frac{1}{2} = \frac{1}{2} - \frac{1}{{512}}\)

\(B \times \frac{1}{2} = \frac{{255}}{{512}}\)

\(B = \frac{{255}}{{512}}:\frac{1}{2}\)

\(B = \frac{{510}}{{512}}\)

Ta có:\(\frac{A}{B} = \frac{{511}}{{512}}:\frac{{510}}{{512}} = \frac{{511}}{{510}}\)

Viết số gồm 3 trăm, 6 đơn vị và 2 phần trăm.