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\(A=\left(-2\right)\left(-1\frac{1}{2}\right).\left(-1\frac{1}{3}\right).\left(-1\frac{1}{4}\right)...\left(-1\frac{1}{214}\right)\)
\(=2.\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{215}{214}=215\)
\(B=\left(-1\frac{1}{2}\right).\left(-1\frac{1}{3}\right).\left(-1\frac{1}{4}\right)....\left(-1\frac{1}{299}\right)\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{300}{299}=\frac{300}{2}=150\)
\(C=-\frac{7}{4}\left(\frac{33}{12}+\frac{3333}{2020}+\frac{3333}{3030}+\frac{333333}{424242}\right)\)
\(=-\frac{7}{4}\left(\frac{33}{12}+\frac{33}{20}+\frac{33}{30}+\frac{33}{42}\right)\)
\(=-\frac{7}{4}.33.\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=-\frac{231}{4}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=-\frac{231}{4}\left(\frac{1}{3}-\frac{1}{7}\right)\)
\(=-\frac{231}{4}.\frac{4}{21}=-11\)
\(A=\frac{\left(1+2+3+...+100\right)\left(\frac{1}{4}+\frac{1}{6}-\frac{1}{2}\right)\left(63.1,2-21.3,6+1\right)}{1-2+3-4+....+99-100}\)
\(=\frac{\frac{100\left(100+1\right)}{2}\left(\frac{3+2-6}{12}\right)\left[63\left(1,2-1,2\right)+1\right]}{\left(1-2\right)+\left(3-4\right)+....+\left(99-100\right)}\)
\(=\frac{5050.\left(-\frac{1}{12}\right).1}{-1+\left(-1\right)+\left(-1\right)+...+\left(-1\right)}\)
\(=\frac{2525.\left(-\frac{1}{6}\right)}{-50}=\frac{101}{12}\)
\(B=\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right).....\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot.....\cdot\frac{10}{9}\cdot\frac{11}{10}\)
\(=\frac{3.4.5.....10.11}{2.3.4....10}=\frac{11}{2}\)
\(=\frac{3.8.15........\left(n-1\right)\left(n+1\right)}{\left(2.3.4.....n\right)\left(2.3.4......n\right)}=\frac{1.3.2.4.3.5..............\left(n-1\right)\left(n+1\right)}{\left(2.3.4.....n\right)\left(2.3.4......n\right)}=\frac{\left(1.2.3......\left(n-1\right)\right)\left(3.4.5......\left(n+1\right)\right)}{\left(2.3.4....n\right)\left(2.3.4.......n\right)}\)
\(=\frac{1.\left(n+1\right)}{n.2}=\frac{n+1}{2n}\)
Bài này mình làm rồi còn gì?