\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+..........+\frac{2}{97.100}=\frac{3}{2}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.........-\frac{1}{100}\right)\)
\(=\frac{3}{2}\times\frac{99}{100}=\frac{297}{200}\)
2/3( giong cai tren nha)
=2/3.99/100=198/300 nha
Trả lời :...........................
\(\frac{198}{300}\)
Hk tốt,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Thử cách này xem:
\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
\(\Rightarrow\frac{3}{2}.A=\frac{3}{2}.\left(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\right)\)
\(\Rightarrow\frac{3}{2}.A=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\)
\(\Rightarrow\frac{3}{2}.A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\)
\(\Rightarrow\frac{3}{2}.A=1-\frac{1}{100}\)
\(\Rightarrow\frac{3}{2}.A=\frac{99}{100}\)
\(\Rightarrow A=\frac{99}{100}:\frac{3}{2}\)
\(\Rightarrow A=\frac{99}{100}.\frac{2}{3}=\frac{33}{50}\)
Thử tham khảo ik, sai thôi nhé !!!
Ukm Trần Hoài Thương
Này :
\(A=\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+...+\frac{2}{97\cdot100}\)
\(A=2\left(\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+...+\frac{1}{97\cdot100}\right)\)
\(3A=2\left(\frac{3}{1\cdot4}+\frac{4}{4\cdot7}+\frac{3}{7\cdot10}+...+\frac{3}{97\cdot100}\right)\)
\(3A=2\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(3A=2\left(1-\frac{1}{100}\right)\)
\(3A=2\cdot\frac{99}{100}\)
\(3A=\frac{99}{50}\)
\(A=\frac{99}{50}\text{ : }3\)
\(A=\frac{33}{50}\)
