19/11 CONG [ 5/13 CONG 3/11 ]
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cho a bang 8 phan 11 nhan 13 cong 8 phan 13 nhan 15 cong ... cong 8 phan 19 nhan 21 va b bang 36 phan 231
Ta có 1/11; 1/12; 1/13;...; 1/39 > 1/40
\(\Rightarrow\) A = 1/11 + 1/12 + 1/13 +...+ 1/39 +1/40 > 1/40 + 1/40 + 1/40 +...+ 1/40 + 1/40(có 30 số hạng)
A > 30/40
Mà 30/40 =3/4 nên A >3/4
Vậy A > 3/4
\(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x.\left(x+3\right)}=\frac{101}{1540}\)
\(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{x.\left(x+3\right)}=\frac{303}{1540}\)
\(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{303}{1540}\)
\(\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1540}\)
\(\frac{1}{x+3}=\frac{1}{308}\)
\(\Rightarrow x+3=308\)
\(x=305\)
\(\frac{4}{5}+\frac{2}{7}+\frac{11}{5}+\frac{12}{7}+\frac{1}{5}\)
\(=\frac{4}{5}+\frac{11}{5}+\frac{1}{5}+\frac{2}{7}+\frac{12}{7}\)
\(=\frac{4+11+1}{5}+\frac{2+12}{7}\)
\(=\frac{16}{5}+\frac{14}{7}\)
\(=\frac{16}{5}+2=\frac{26}{5}\)
\(\frac{4}{5}+\frac{2}{7}+\frac{11}{5}+\frac{12}{7}+\frac{1}{5}\)
\(=\left(\frac{4}{5}+\frac{11}{5}+\frac{1}{5}\right)+\left(\frac{2}{7}+\frac{12}{7}\right)\)
\(=\frac{16}{5}+\frac{14}{7}\)
\(=\frac{16}{5}+2=\frac{16}{5}+\frac{10}{5}=\frac{26}{5}\)
\(\frac{19}{11}+\left(\frac{5}{13}+\frac{3}{11}\right)\)
\(=\frac{19}{11}+\frac{3}{11}+\frac{5}{13}\)
\(=\frac{19+3}{11}+\frac{5}{13}\)
\(=\frac{22}{11}+\frac{5}{13}=2+\frac{5}{13}\)
\(=\frac{26}{13}+\frac{5}{13}=\frac{31}{13}\)
Tính
\(\frac{19}{11}+\left(\frac{5}{13}+\frac{3}{11}\right)\)
\(=\frac{19}{11}+\frac{5}{13}+\frac{3}{11}\)
\(=\frac{5}{13}+\left(\frac{19}{11}+\frac{3}{11}\right)\)
\(=\frac{5}{13}+2=\frac{5}{13}+\frac{26}{13}=\frac{31}{13}\)