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A) \(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{10101\times13}{10101\times15}+\frac{10101\times13}{10101\times35}+\frac{10101\times13}{10101\times63}+\frac{10101\times13}{10101\times99}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13\times\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=13\times\frac{4}{33}=\frac{52}{33}\)
B) \(\left(1998:18-1443:13\right)\times\left(16996-1110:30\times305\right)\)
\(=\left(111-111\right)\times\left(16996-1110:30\times305\right)\)
\(=0\times\left(16996-1110:30\times305\right)\)
\(=0\)
( TẤT CẢ MỌI SỐ NHÂN VỚI 0 ĐỀU BẰNG 0)
C) \(\left(\frac{575757}{424242}+\frac{575757}{565656}+\frac{575757}{727272}\right)\times18\)
\(=\left(\frac{10101\times57}{10101\times42}+\frac{10101\times57}{10101\times56}+\frac{10101\times57}{10101\times72}\right)\times8\)
\(=\left(\frac{57}{42}+\frac{57}{56}+\frac{57}{72}\right)\times8\)
\(=\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\times57\times8\)
\(=\frac{1}{169344}\times57\times8\)
\(=\frac{19}{7056}\)
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a, = 13/15 + 13/35 + 13/63 + 13/99
= 13.( 1/15 + 1/35 + 1/63 + 1/99 )
= 13.( 1/ 3.5 + 1/5.7 + 1/7.9 + 1/ 9.11)
= 13 . ( 1/3 - 1/5 +1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11)
= 13 . ( 1/3 - 1/11)
= 13 . 3/11 = 39/11
Bài 2:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
\(B=70.\left(\frac{131313}{565656}+\frac{131313}{727272}+\frac{131313}{909090}\right)\)
\(B=70.\left(\frac{13}{56}+\frac{13}{72}+\frac{13}{90}\right)\)
\(B=70.13.\left(\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(B=910.\left(\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(B=910.\left(\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(B=910.\left[\frac{1}{7}+\left(\frac{1}{8}-\frac{1}{8}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)-\frac{1}{10}\right]\)
\(B=910.\left[\frac{1}{7}-\frac{1}{10}\right]\)
\(B=910.\frac{3}{70}=39\)
~ Hok tốt ~
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot.....\cdot\frac{2014}{2013}\)
\(=\frac{2}{2013}\)
\(A=\frac{12\cdot10101}{13\cdot10101}+\frac{14\cdot11011}{13\cdot11011}-\left(\frac{21\cdot101}{23\cdot101}+\frac{25\cdot11011}{23\cdot11011}\right)\)
\(A=\frac{12}{13}+\frac{14}{13}-\left(\frac{21}{23}+\frac{25}{23}\right)\)
\(A=0\)
nhớ cho đúng nha
\(A=\frac{121212}{131313}+\frac{154154}{143143}-\left(\frac{2121}{2323}+\frac{275275}{253253}\right)\)
\(\Leftrightarrow A=\frac{12}{13}-\frac{14}{13}-\left(\frac{21}{23}+\frac{25}{23}\right)\) (Áp dụng phương pháp rút gọn phân số)
\(\Leftrightarrow A=\frac{12}{13}-\frac{14}{13}-\frac{46}{23}=\frac{\left(-2\right)}{13}-\frac{46}{23}\)
\(\Leftrightarrow A=-\frac{28}{13}\)