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=\(\dfrac{4}{3}+\dfrac{9}{8}+\dfrac{16}{15}+...+\dfrac{100}{99}\)
=\(\frac{2.2}{1.3}\)+\(\frac{3.3}{2.4}\)+.....+\(\frac{10.10}{9.11}\)
=\(\frac{2.3......10}{1.2.3.....9}\)+\(\frac{2.3.4....10}{3.4.5......11}\)
=\(10+\dfrac{2}{11}\)
=\(10\frac{2}{11}\)
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.1\frac{1}{24}...1\frac{1}{99}\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}....\frac{100}{99}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{10.10}{9.11}\)
\(=\frac{2.2.3.3.4.4.5.5....10.10}{1.3.2.4.3.5.4.6....9.11}\)
\(=\frac{\left(2.3.4.5....10\right)\left(2.3.4.5...10\right)}{\left(1.2.3.4.5...9\right)\left(3.4.5.6...11\right)}\)
\(=\frac{10.2}{11}\)
\(=\frac{20}{11}\)
Có gì không hiểu cứ hỏi nhé. Học tốt <3
\(\frac{1}{2}-\frac{1}{3}\cdot\frac{1}{4}\)
=\(\frac{1}{2}-\frac{1}{3.4}\)
=\(\frac{1}{2}-\frac{1}{12}\)
=\(\frac{6}{12}-\frac{1}{12}\)
=\(\frac{6-1}{12}\)
=\(\frac{5}{12}\)
\(\frac{1}{3}\times\frac{1}{6}\times\frac{1}{9}=\frac{1\times1\times1}{3\times6\times9}=\frac{1}{162}\)
\(\frac{1}{3}\times\frac{1}{6}:\frac{1}{9}=\frac{1}{3}\times\frac{1}{6}\times\frac{9}{1}=\frac{1\times1\times9}{3\times6\times1}=\frac{9}{18}=\frac{1}{2}\)
Tự tính câu cuối đi
=4/3+9/8+16/15+........+100/99
=\(\frac{2.2}{1.3}\)+\(\frac{3.3}{2.4}\)+.....+\(\frac{10.10}{9.11}\)
=\(\frac{2.3......10}{1.2.3.....9}\)+\(\frac{2.3.4....10}{3.4.5......11}\)
=10+2/11
=\(10\frac{2}{11}\)