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Bài 1:
\(=\dfrac{-1}{2}+\dfrac{3}{5}-\dfrac{1}{9}+\dfrac{1}{131}+\dfrac{2}{7}+\dfrac{4}{35}-\dfrac{7}{18}\)
\(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{131}\)
\(=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}+\dfrac{1}{131}\)
=1/131
Bài 2:
b: \(B=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)
\(=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{99}-\dfrac{98}{99}=-\dfrac{97}{99}\)
\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)....\left(\frac{1}{121}-1\right)=-\frac{3}{4}.-\frac{8}{9}....-\frac{120}{121}=\frac{-1.3}{2.2}\cdot\frac{-2.4}{3.3}....-\frac{10.12}{11.11}=\frac{-1}{2}.-\frac{12}{11}=\frac{6}{11}\)
\(\frac{\frac{2}{3}+\frac{2}{5}+\frac{2}{7}+\frac{2}{9}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}+\frac{11}{9}}=\frac{2\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}{11\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}=\frac{2}{11}\)
\(\frac{\frac{2}{3}+\frac{2}{5}+\frac{2}{7}+\frac{2}{9}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}+\frac{11}{9}}\)
=\(\frac{2\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}{11\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}\)
=\(\frac{2}{11}\)
\(\frac{\frac{2}{3}+\frac{2}{5}+\frac{2}{7}+\frac{2}{9}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}+\frac{11}{9}}=\frac{2\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}{11\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)}=\frac{2}{11}\)
\(\text{1+1+1+1+1+1+1+1+11+1+9=}29\)
\(HokT\)
29 nha!