\(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}=\frac{\left(2.3...29.30\right).\left(3.4.5...29.31\right)}{\left(2.3...29.30\right).\left(2.3.4...29.30\right)}=\frac{31}{2.30}=\frac{31}{60}\)

Gjngkbb. Mk

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}\frac{3.5}{4.4}.....\frac{29.31}{30.30}=\frac{\left(1.2.3....29\right)\left(3.4.5....31\right)}{\left(2.3.4....30\right)\left(2.3.4....30\right)}=\frac{31}{30.2}=\frac{31}{60}\)

\(A=\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)

\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{899}{900}\)

\(=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)

\(=\frac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot...\cdot30}\cdot\frac{3\cdot4\cdot5\cdot...\cdot31}{2\cdot3\cdot4\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)

A\(=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}=\frac{3.8.15...899}{2^2.3^2.4^2...30^2}=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)

  \(=\)\(\frac{\left(1.2.3...29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}=\frac{1.2.3...29}{2.3.4...30}.\frac{3.4.5...31}{2.3.4...30}=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

=> A= \(\frac{31}{60}\)

đúng cái nhé

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yWahorSNPE0lr0m2kcXB3EcCCOBByIkE28F4i8O8A7wQoV4AMSYZiSYAghXhSB6cnWnS4wWFrYq1yi+yDuLsQqA9NplnWlL7XL/7Nq/t0b/2q/lAw+viWdjUdizMxZmO9mJuSfOOKbyEXtHaVbOaE1Y4pjKNHBKh4iDZh0zFkQGcQxVSVFz/ADeRMMiEXUnPPImTzOdiMOVYvT814Hw5GA6KeyePxjhiMPiQwIIz65EH+fvjtoHT1b09WwNZcRRaxG8G+y68UccQfQ2O8TatOYnC4tMJjWXbR6b7F2YBSxQurBTYsCAM+KmYARLpqLpumVGAxI2qfeirRzYBXKlXQ2OatcNbddTzmc/HTiusovQwGBe5AZfCq5H2SxEl6I0dQR9qnVKnltsNryORjFTVXRrN3l6ynK4SvVVfshsp1qFLDU7KhOW7aYsftNnPNY920lsUwOY8wb+kFTGoFLtaygk3yIsJHxWNUEBRckjeQq58rKST5W6icvTmOw5PdsSKYG3XdhsqtJT7QubZsbILby/jLJXK2T1m/aji+8x2xfOlh6FM9G2O9bzvVMqUkaUx74mtVxL/AEqtRnI5bTE7PgL28pGBnqeOlWnW0FrPisCCtCpZWIYoyhlJAtfMXFwADYjcOQnIvEMYRv8AgdbcFUSm3ymgrOqHZaooKswB2Dc5MCbWOdxO2DxnmUjhLHq3rjisCNhCHp8KdS7Kv7BBBXwBt0vJobveAmVLVfX3D40ik/zNY5BGN1c/0b8T+qbHleWtjIoExJMK8STAO8OIvBIJUrPaPhO+0biVG9UFT+yZah9EMs04+tzEYHFkb/kuI/wXgeaHGcfRY3bOSEE0HaccBjaxwGUOoY+TIyxyo1rGEBokJC7y8UIDdeiDnuPA8fPp0jOFxNyUbJhw/ESS05ukaBycbxA6LCJGXjwkbAYwP7Jyb75LIgatq1oF9I4VMRRxdVWHsVKZY2R13jI7iCGHRhO9q/qrW2K+Hr1H7wENTqBi3sMABYnPerZTOuzXWj5BibVGtQq2Srfcnu1f3STfoTyE3+nlUJ5oPRj/AOUajX3l+2V4jD4jDpX22ZzTBKkHZ2rC9gSDa/Mgyh6y64HSC06KUe5QWet7feGq6iybTAAFRckCwFze03PT+GDCoLfSS3oZ5UNR8O70xwYqb/qkiTUhcrXVqZRNzu3Hkcj6xnCaUAZXORB6EEbj9LLjxnapVu+BXa2y52mDXFY7I+qq3By4gnra0u2XMBipIxOFUC6vnn82wO2FzzJ8uPMSKDAXFAxomDagEZY9F694/DjZFbvF4CuO8t+9cP8A9UrsSYGw6t9pGHxJFLED5PVJsCTekx6P9TwbLqZdTPMxmodmOt5cjAV2ubfMOTmQB+iY8TYHZPS3K8sGjwRUEyqRIOnKYfD10O5qNUfGmw/GTpyta65p4LFVBvXD1iPHu2t62gea0zkhZHXkJIWaCxFRIihKFqY5a4I6RoR2m1oRHpteSEkBmsxHUyVSeBIMbqLcWiwYoCBwcZhih2h/pJ2BxocbJ+l98nPSDCxnGxeAZPaX/SFdgTaeyXWr5RTGDqm9Wih2Cfr0fZt5oQB4FeswnAY0P7LZN987GitIVMNWp4ikbPTYMp4ciCORBIPQmEelMbR2jPMWveie6x+KpjhWY/bAqf556Z0FpenjsNTxVLcw9peKOPpI3UH45HjMU7XcIKek6jW/SU6Lnqdnu/8Aty3sZS6Fd8VSrsu7dyO6dTStD2Qw33/AzkETKuvS0wSopsSFHQfAtbaI6EkCSKbqdxlfi6bkbo2O+VidmcynjGHX75Lp6QXiCJdokARDxxKituIgdIDN4dGs1Ng6GzKwZTyZTdT5ECJKwjA1f/3XX/giFMqtBCaeopVu03Fmlo3EEb2C0/Ko6o3oTLTKh2roToytbg1Enw75P4zDbBaQkhZHDZyQDNIcECwjBTlDojqxoGLEI5eMa1RvEfcJJwj5SJpD9IfARdBrSK6yCKJkBaxjqVJRKEURGdqEtWERsZo0H2kyb0hYTFG/duLN98nCpI+Nw/eL1G4wNF7HtOmhijhGPzeIGXIVkBKkctpdpepC8pI7c6IGIw1X36Lr/ZuD/wB2ZdojSbo6m+zVpsrIf1kIZT43AmrdrmMTFYPA4xBYMWt072mr7PkaZH7ssGXVluLdZDqYUSaDDIvIObo7RXf4ilh9rZ7yoibRF9naYC9uO+XLHdkuOS/dtRqjo5Rj5OLes4ehFtjMMf8AmcP/AIqz0dsSVXmDTGruKwn6ehUpjgxF08qi3X1kCnVPTwnq1qQIIIBB3g5g+IlT052b4DE3Ipdw5+vR9n40/oH4A9ZBgYxI4p5j+McXHctoePtfnLzpjsmxdK7YepTrjkfmqnqdk/alTxuruNoG1TDV16imXX7SixlEZMZfeD452hs2Vxnytx6DrLBq1qFjcb7RvRp+/VBW/wCxTtdvQdZpOq/ZxhsG4rVGOIqqQVLAKiEfWVATdupJtwtGxy//AEG3u+hgmkXgj6TSTKt2nUi2jMQBwFNvJayMfQGWiQdOYMV8PWoHdUpVE8NpCL+V7zLbzHTGd4+kYp7geefxkmiJpkbtF0hGWzYCSBAXaLEbBiwJUcjSLWqHwEbpYi0VjkvUby+4RsYeRU6niAY8rgyAmFkmkmzKHy8AMSBFAwFBo8jxiKWBH0ph7jvF3jM2naoawivotsDUPt0K6VqXVWLpUUeDVtrzPKQAOE4tegabdPwMI69I5RcYwTXQGOsYE3QKbWLww/5ih/irPRYmAak0dvH4Zf6ZT9j2/wDLN/ElCoRhwpFIIiSIsxJgItCMUYkyArwQQQJUSYcSYaeZNK4buq1Wj7lWonkjlfwiENp19eqezpDFD+mY/as34ziMeErJdAcY9EothDlC1jimIEWJUQKi/ON5fdDtaN1alqh8fwEeFUQpu8UDD9mLUjnAIXgDRQZecbqniIDgaOAyAahEUmIPKB0RGcYl1PO0KlViqz5QhrRv6P4x8xjRp+bjxgWvswobekaR9xarf/my/wCabeJjPZP/AL+P6qr+H8JswkqjghwSBJiCI4YgwEGIIjhiDIEwQ4IEiFBBI08+don/ANniv6xf8KnK8N8EE3GUpYSQQQHBFwQSo42K/SN4/wAI0YUEigYkwQQCEl0d3884IID8VBBAepxGJ3GCCUFov6H8846YIIRdeyv/AH9P6ur/AHZtAggmaDEEOCFJMSYIJAgxBgggFBBBA//Z" 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Đặt \(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)

\(\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{29.31}{30.30}\)

\(\Rightarrow A=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)

\(\Rightarrow A=\frac{\left(1.2.3...29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}\)

\(\Rightarrow A=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

Vậy \(A=\frac{31}{60}\)