Question

[Ngô Anh Dũng]

Các bạn giúp mình nha!!

Answer 1

[Nguyên Anh]

a) A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\)

A = \(1-\frac{1}{8}\)

A = \(\frac{7}{8}\)

b) B =  \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+\frac{1}{4.5.6}+\frac{1}{5.6.7}+\frac{1}{6.7.8}+\frac{1}{7.8.9}\)

B = \(\frac{1}{2}.\left(\frac{2}{1.2}-\frac{2}{2.3}+\frac{2}{2.3}-\frac{2}{3.4}+...+\frac{2}{7.8}-\frac{2}{8.9}\right)\)

B = \(\frac{1}{2}.\left(\frac{2}{1.2}-\frac{2}{8.9}\right)\)

B = \(\frac{1}{2}.\frac{35}{36}=\frac{35}{72}\)

Answer 2

[Phương An]

\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}\)

   \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}=1-\frac{1}{8}=\frac{7}{8}\)

\(B=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+\frac{1}{4\times5\times6}+\frac{1}{5\times6\times7}+\frac{1}{6\times7\times8}+\frac{1}{7\times8\times9}\)

\(2B=\frac{2}{1\times2\times3}+\frac{2}{2\times3\times4}+\frac{2}{3\times4\times5}+\frac{2}{4\times5\times6}+\frac{2}{5\times6\times7}+\frac{2}{6\times7\times8}+\frac{2}{7\times8\times9}\)

      \(=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+\frac{1}{3\times4}-\frac{1}{4\times5}+\frac{1}{4\times5}-\frac{1}{5\times6}+\frac{1}{5\times6}-\frac{1}{6\times7}+\frac{1}{6\times7}-\frac{1}{7\times8}+\frac{1}{7\times8}-\frac{1}{8\times9}\)

      \(=1-\frac{1}{72}\)

      \(=\frac{71}{72}\)

\(B=\frac{71}{72}\times\frac{1}{2}=\frac{71}{144}\)