\(A=\frac{1}{71}+\frac{2}{70}+\frac{3}{69}+\frac{4}{68}+...+\frac{70}{2}+\frac{71}{1};B=\frac{1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{71}+\frac{1}{72}}AxB=?\)
Những câu hỏi liên quan
Chứng minh rằng số tự nhiên \(A=1\times2\times3\times...\times69\times70\times\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{70}\right)⋮71\)
Ta có:
\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{70}=\left[1+\frac{1}{70}\right]+\left[\frac{1}{2}+\frac{1}{69}\right]+\left[\frac{1}{3}+\frac{1}{68}\right]+...+\left[\frac{1}{35}+\frac{1}{36}\right]\)
\(=\frac{71}{1.70}+\frac{71}{2.69}+\frac{71}{3.68}+...+\frac{71}{35.36}\)
\(=71\left[\frac{1}{1.70}+\frac{1}{2.69}+\frac{1}{3.68}+...+\frac{1}{35.36}\right]⋮71\)
=> \(A=1\times2\times3\times4\times...\times70\times\left[1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{70}\right]⋮71\)=> ĐPCM
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Xét \(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{70}=\left(1+\frac{1}{70}\right)+\left(\frac{1}{2}+\frac{1}{69}\right)+...+\left(\frac{1}{35}+\frac{1}{36}\right)\)
\(=\frac{71}{1.70}+\frac{71}{2.69}+...+\frac{71}{35.36}=71\left(\frac{1}{1.70}+\frac{1}{2.69}+...+\frac{1}{35.36}\right)\)
=>\(A=1.2.3.4...71.\left(\frac{1}{1.70}+\frac{1}{2.69}+...+\frac{1}{35.36}\right)⋮71\)
Vậy A chia hết cho 71
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Xem thêm câu trả lời
tính A=\(\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{1}{85}+\frac{3}{50}+\frac{3}{65}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
A=\(\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{1}{34}+\frac{3}{20}-\frac{3}{26}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
\(=\dfrac{52}{9}\)
Cái này mk tính bằng máy nên không biết cách làm đâu!!!
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Tính bằng cách thuận tiện
1,\(\frac{13}{19}\left(\frac{19}{26}-\frac{71}{43}\right)+\frac{71}{43}\left(\frac{13}{19}-\frac{86}{71}\right)\)
2,\(\frac{5}{7}\left(\frac{1}{2}-\frac{1}{3}+\frac{4}{7}\right)+\left(\frac{1}{2}-\frac{1}{3}-\frac{4}{7}\right):\frac{7}{5}\)
\(A=\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{1}{34}+\frac{3}{20}-\frac{3}{26}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
http://olm.vn/hoi-dap/question/194836.html
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Tính \(A=\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{3}{26}-\frac{3}{20}-\frac{1}{34}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
Tính A = \(\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{3}{26}-\frac{3}{20}-\frac{1}{34}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
Tính A theo cách hợp lý: \(A=\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{3}{26}-\frac{3}{20}-\frac{1}{34}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
A = \(\frac{4\left(\frac{1}{78}-\frac{1}{60}-\frac{1}{306}\right)}{9\left(\frac{1}{78}-\frac{1}{60}-\frac{1}{306}\right)}:\frac{1+\frac{2}{71}-\frac{5}{121}}{-13\left(1+\frac{2}{71}-\frac{5}{121}\right)}=\frac{4}{9}:-\frac{1}{13}\)
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Tính:
\(A=\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{1}{34}+\frac{3}{20}-\frac{3}{26}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
