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=(5/30+3/30+2/30) : (5/30+3/30-2/30)
=10/30 : 5/30
=10/30 x 30/5
=2
!!! Hok tốt!!!
\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}\right)\)
=\(\frac{10}{30}:\frac{6}{30}\)
\(=\frac{5}{3}\)
Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}\)
\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}\)
\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{7}-\frac{1}{8}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{8}\right)\)
\(\Rightarrow A=2\cdot\frac{3}{8}=\frac{3}{4}\)
\(S=\frac{1}{3}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{300}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{6}+\frac{1}{12}+\cdot\cdot\cdot+\frac{1}{600}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{2\times3}+\frac{1}{3\times4}+\cdot\cdot\cdot+\frac{1}{24\times25}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdot\cdot\cdot+\frac{1}{24}-\frac{1}{25}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{2}-\frac{1}{25}\)
\(\Rightarrow\frac{1}{2}S=\frac{23}{50}\)
\(\Rightarrow S=\frac{23}{50}:\frac{1}{2}\)
\(\Rightarrow S=\frac{23}{25}\)
S = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{300}\)
= \(2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{600}\right)\)
= \(2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{24\times25}\right)\)
= \(2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{24}-\frac{1}{25}\right)\)
= \(2\times\left(\frac{1}{2}-\frac{1}{25}\right)\)
\(=2\times\frac{23}{50}\)
\(=\frac{23}{25}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{5050}=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{10100}\right)\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{100.101}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{100}-\frac{1}{101}\right)=2.\frac{99}{202}=\frac{99}{101}\)
Đặt A = 1/3+1/6+1/10+1/15+...+1/5050
A : 2 ta có : 1/6+1/12+1/20+1/30+...+1/10100
A: 2 = 1/2x3+1/3x4+1/4x5+1/5x6+..... + 1/ 100 x 101
A: 2 = 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...1/100-1/101
Rút gọn ta được :
A: 2 = 1/2-1/101
A: 2 = 99/202
A = 99/202x2 = 99 / 101