Question

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

PLS...

Answer 1

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

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

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

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

\(=\dfrac{3}{6}-\dfrac{1}{6}\)

\(=\dfrac{2}{6}=\dfrac{1}{3}\)

Answer 2

1/2 x 1/3 + 1/3 x 1/4 + 1/4 x 1/5 + 1/5 x 1/6
= 1/6 + 1/12 + 1/20 + 1/30
= (10/60) + (5/60) + (3/60) + (2/60)
= 20/60 + 10/60 + 6/60 + 4/60
= 40/60
= 2/3
Vậy giá trị của biểu thức là 2/3.