\(\frac{1}{1}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

                                                                                           \(=\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{3}{60}+\frac{2}{60}\)

                                                                                          \(=\frac{50}{60}=\frac{5}{6}\)

Đáp án là 5/6 tick nha bạn

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

= \(1-\frac{1}{6}=\frac{5}{6}\)

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

\(=\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\frac{1}{6}\)

\(=0+0+0+0+\frac{1}{6}\)

\(=\frac{1}{6}\)

_Chúc bạn học tốt_

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

\(=\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\frac{1}{6}\)

\(=0+0+0+0+\frac{1}{6}\)

\(=\frac{1}{6}\)

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

\(=\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\frac{1}{6}\)

\(=0+0 +0+0+\frac{1}{6}\)

\(=\frac{1}{6}\)

a) 1/2

b) 3/8

~~~~~~~~~hok tốt~~~~~~~~~~~~

A/ \(\frac{1}{2}\)

B/ \(\frac{3}{8}\)  

suy ra 1-1/6=5/6

\(\frac{1}{2}-\frac{1}{-3}+\frac{1}{-3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{-5}+\frac{1}{-5}.\frac{1}{6}\)1/6

\(=\frac{1}{2}+\frac{1}{3}-\frac{1}{3}.\frac{1}{4}+\left(\frac{1}{4}+\frac{1}{6}\right).\frac{-1}{5}\)

\(=\frac{5}{6}-\frac{1}{12}+\frac{5}{6}.\frac{-1}{5}\)

\(=\frac{7}{12}\)

\(\dfrac{2}{5}+\dfrac{1}{4}=\dfrac{8}{20}+\dfrac{5}{20}=\dfrac{13}{20}\)
\(\dfrac{1}{3}+\dfrac{3}{5}=\dfrac{5}{15}+\dfrac{9}{15}=\dfrac{14}{15}\)
\(\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}\)
\(\dfrac{1}{8}+\dfrac{5}{6}=\dfrac{3}{24}+\dfrac{20}{24}=\dfrac{23}{24}\)

ĐÂSDWADAS

1/2 × 1/2 + 1/2 × 1/3 + 1/3 × 1/4 + 1/4 × 1/5 + 1/5 × 1/6

= 1/4 + 1/2×3 + 1/3×4 + 1/4×5 + 1/5×6

= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

= 1/4 + 1/2 - 1/6

= 3/12 + 6/12 - 2/12

= 9/12 - 2/12

= 7/12

1/2×1/2+1/3×1/3+1/4×1/4+1/5×1/5+1/6×1/6

phải k ạ

\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)

\(=\frac{1}{2\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)

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

\(=\frac{1}{2}-\frac{1}{6}\)

\(=\frac{1}{3}\)