5 ngày 7 giờ=....127...giờ

285 phút=...4,75.....giờ

1/4 phút=...15...giây

3/4 giờ=..45...phút

1/6 ngày=..4..giờ

3,75 giờ=...225..phút

0,4 giờ=....24...phút

2 giờ 12 phút=........2,2......giờ

Ta đã biết \(\dfrac{1}{a\cdot a}< \dfrac{1}{\left(a+1\right)\left(a-1\right)}\) ( a ϵ Z )

⇒ \(Q=\dfrac{1}{2\cdot2}+\dfrac{1}{3\cdot3}+\dfrac{1}{4\cdot4}+...+\dfrac{1}{200\cdot200}\) < \(\dfrac{1}{1\cdot3}+\dfrac{1}{2\cdot4}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{199\cdot201}\) 

Ta có \(\dfrac{1}{1\cdot3}+\dfrac{1}{2\cdot4}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{199\cdot201}\) 

= \(\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{2\cdot4}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{199\cdot201}\right)\)

= \(\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{199}-\dfrac{1}{201}\right)\)

= \(\dfrac{1}{2}\left(1-\dfrac{1}{201}\right)=\dfrac{1}{2}\cdot\dfrac{200}{201}=\dfrac{100}{201}< \dfrac{100}{200}=\dfrac{1}{2}< \dfrac{3}{4}\)

Vậy Q < \(\dfrac{3}{4}\)

A = \(\dfrac{4}{1\times3}\) - \(\dfrac{8}{3\times5}\) + \(\dfrac{12}{5\times7}\) - \(\dfrac{16}{7\times9}\) + \(\dfrac{20}{9\times11}\) - \(\dfrac{24}{11\times13}\)

A = ( \(\dfrac{1}{1}+\dfrac{1}{3}\)) - ( \(\dfrac{1}{3}\) + \(\dfrac{1}{5}\)) + (\(\dfrac{1}{5}\)+ \(\dfrac{1}{7}\)) - ( \(\dfrac{1}{7}\) + \(\dfrac{1}{9}\)) +( \(\dfrac{1}{9}\)+ \(\dfrac{1}{11}\)) - (\(\dfrac{1}{11}\)+\(\dfrac{1}{13}\))

A = \(\dfrac{1}{1}+\dfrac{1}{3}\) - \(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{7}\) - \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{11}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{12}{13}\)

\(\dfrac{-3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)=\dfrac{-3}{17}+\dfrac{2}{3}+\dfrac{3}{17}=\left(\dfrac{-3}{17}+\dfrac{3}{17}\right)+\dfrac{2}{3}=0+\dfrac{2}{3}=\dfrac{2}{3}\)

9,12 x 6 + 91,2 - 9,12 : 0,5 - 9,12 : 0,25

= 9,12 x 6 + 10 x 9,12 - 9,12 x 2 - 9,12 x 4

= 9,12 x ( 6 + 10 - 2 - 4 )

= 9,12 x 10 = 91,2

Ta có : 1+9+2+8+3+7+4+6+5=?

   ==>  1+2+3+4+5+6+7+8+9=?

       Số số hạng phép tính trên có là:(9-1):1+1=9(số hạng)

       Tổng : (9+1)x9:2 = 45

    Chúc bn học giỏi! :3

45

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