A = \(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.\frac{24}{5^2}...\frac{899}{30^2}\)
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Những câu hỏi liên quan
\(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.\frac{24}{5^2}.....\frac{899}{30^2}\)
\(A=\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)
\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{899}{900}\)
\(=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot...\cdot30}\cdot\frac{3\cdot4\cdot5\cdot...\cdot31}{2\cdot3\cdot4\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)
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Tính tích:
\(A=\frac{3}{\sqrt[2]{2}}x\frac{8}{\sqrt[2]{3}}x\frac{15}{\sqrt[2]{4}}x\frac{24}{\sqrt[2]{5}}x....x\frac{899}{\sqrt[2]{30}}\)
1\(\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\)\(1\frac{1}{\frac{2}{4.x-\frac{1}{2}}}-\frac{3}{4}\)=\(\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)ai nhanh mik tick
\(A=\frac{3}{2^2}.\frac{8}{3^2}\frac{15}{4^2}.....\frac{899}{30^2}\)
\(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.....\frac{899}{30^2}\)
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= \(\frac{31}{60}\)
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Bài 1 : tính
a) \(\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)
b) \(\frac{\left(\frac{3}{4}+\frac{3}{7}-\frac{3}{8}\right)}{\frac{5}{4}+\frac{5}{7}-\frac{5}{8}}\)
Tính \(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}....\frac{899}{30^2}\)
![[A]ȵȟ•βê•ʠǔá♡](https://hoc24.vn/images/avt/avt1063100_256by256.jpg)
Rút gọn:
\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}\frac{3.5}{4.4}.....\frac{29.31}{30.30}=\frac{\left(1.2.3....29\right)\left(3.4.5....31\right)}{\left(2.3.4....30\right)\left(2.3.4....30\right)}=\frac{31}{30.2}=\frac{31}{60}\)
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\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)