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15 tháng 3 2023

A=(-1/4.5)+(-1/5.6)+(-1/6.7)+(-1/7.8)+(-1/8x9)+(-1/9.10)

A=(-1/4)-(-1/5)+(-1/5)-(-1/6)+(-1/6)-(-1/7)+(-1/7)-(-1/8)+(-1/8)-(-1/9)-(-1/9)+(-1/10)

A=(-1/4)-(-1/10)

A=-1/4+1/10

A=-3/20

AH
Akai Haruma
Giáo viên
31 tháng 12 2018

Lời giải:

a)

\(A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+....+\frac{-1}{90}\)

\(=\frac{-1}{4.5}+\frac{-1}{5.6}+\frac{-1}{6.7}+...+\frac{-1}{9.10}\)

\(=\frac{4-5}{4.5}+\frac{5-6}{5.6}+\frac{6-7}{6.7}+....+\frac{9-10}{9.10}\)

\(=\frac{1}{5}-\frac{1}{4}+\frac{1}{6}-\frac{1}{5}+\frac{1}{7}-\frac{1}{6}+...+\frac{1}{10}-\frac{1}{9}\)

\(=\frac{1}{10}-\frac{1}{4}=-\frac{3}{20}\)

b)

\(2B=5+\frac{8}{11}+\frac{3}{11}+\frac{1}{15}+\frac{13}{15.2}\)

\(=5+\frac{11-3}{11}+\frac{3}{11}+\frac{1}{15}+\frac{15-2}{15.2}\)

\(=5+1-\frac{3}{11}+\frac{3}{11}+\frac{1}{15}+\frac{1}{2}-\frac{1}{15}\)

\(=5+1+\frac{1}{2}=\frac{13}{2}\Rightarrow B=\frac{13}{4}\)

31 tháng 12 2018

Thanks

mk làm câu a cách khác ; nhưng cũng = \(\dfrac{-3}{20}\)

14 tháng 4 2023

A = \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\) + \(\dfrac{1}{72}\) + \(\dfrac{1}{90}\) + \(\dfrac{1}{110}\) + \(\dfrac{1}{132}\)

A = \(\dfrac{1}{4\times5}\) + \(\dfrac{1}{5\times6}\) + \(\dfrac{1}{6\times7}\)\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\)\(\dfrac{1}{9\times10}\) + \(\dfrac{1}{10\times11}\)+\(\dfrac{1}{11\times12}\)

A = \(\dfrac{1}{4}\)-\(\dfrac{1}{5}\) +\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\) +.....+\(\dfrac{1}{11}\) - \(\dfrac{1}{12}\)

A = \(\dfrac{1}{4}\) - \(\dfrac{1}{12}\)

A = \(\dfrac{1}{6}\)

 

2 tháng 8 2017

\(A=\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)

\(=-\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)

\(=-\left(\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\)

\(=-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(=-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)\)\(=-\dfrac{3}{20}\)

2 tháng 8 2017

Bài 1. ko quy đồng hãy tính hợp lý:

\(A=\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)

\(A=\dfrac{-1}{4.5}+\dfrac{-1}{5.6}+\dfrac{-1}{6.7}+\dfrac{-1}{7.8}+\dfrac{-1}{8.9}+\dfrac{-1}{9.10}\)

\(A=\dfrac{-1}{4}-\dfrac{-1}{5}+\dfrac{-1}{5}-\dfrac{-1}{6}+\dfrac{-1}{6}-\dfrac{-1}{7}+\dfrac{-1}{7}-\dfrac{-1}{8}+\dfrac{-1}{8}-\dfrac{-1}{9}+\dfrac{-1}{9}-\dfrac{-1}{10}\)

\(A=\dfrac{-1}{4}-\dfrac{-1}{10}\)

\(A=\dfrac{-3}{20}\)

27 tháng 5 2022

`[-1]/2+[-1]/6+[-1]/12+[-1]/20+[-1]/30+[-1]/42+[-1]/56+[-1]/72+[-1]/90`

`=(-1)(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)`

`=(-1)(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)`

`=(-1)(1-1/10)`

`=(-1). 9/10=-9/10`

27 tháng 5 2022

A = \(\dfrac{-1}{2}\) + \(\dfrac{-1}{6}\)\(\dfrac{-1}{12}\)\(\dfrac{-1}{20}\)\(\dfrac{-1}{30}\)\(\dfrac{-1}{42}\)\(\dfrac{-1}{56}\)\(\dfrac{-1}{72}\)\(\dfrac{-1}{90}\)

A = \(\dfrac{-1}{2}\) + \(\dfrac{-1}{2\times3}\)\(\dfrac{-1}{3\times4}\)\(\dfrac{-1}{4\times5}\)\(\dfrac{-1}{5\times6}\)\(\dfrac{-1}{6\times7}\)\(\dfrac{-1}{7\times8}\)\(\dfrac{-1}{8\times9}\)+ + \(\dfrac{-1}{9\times10}\)

A = - (\(\dfrac{1}{2}\)\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)\(\dfrac{1}{4}\)\(\dfrac{1}{5}\)\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)\(\dfrac{1}{6}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\)+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\)\(\dfrac{1}{9}\)-\(\dfrac{1}{10}\))

A = -(1-\(\dfrac{1}{10}\))

A = \(\dfrac{-9}{10}\)

12 tháng 9 2021

\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\\ =\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\\ =\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\\ =\dfrac{1}{3}-\dfrac{1}{9}\\ =\dfrac{2}{9}\)

12 tháng 9 2021

\(a,\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\)

\(=\dfrac{1}{212}\)

=9/10-(1/2+1/6+...+1/90)

=9/10-(1-1/2+1/2-1/3+...+1/9-1/10)

=9/10-9/10=0

30 tháng 5 2023

D = 1 + \(\dfrac{-1}{20}\) + \(\dfrac{-1}{30}\) + \(\dfrac{-1}{42}\)\(\dfrac{-1}{56}\)\(\dfrac{-1}{72}\)\(\dfrac{-1}{90}\)

D = 1 - ( \(\dfrac{1}{4\times5}\) + \(\dfrac{1}{5\times6}\)\(\dfrac{1}{6\times7}\)\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\)+\(\dfrac{1}{9\times10}\))

D = 1 - ( \(\dfrac{1}{4}\) - \(\dfrac{1}{10}\))

D = 1 - \(\dfrac{3}{20}\)

D = \(\dfrac{17}{20}\)

30 tháng 5 2023

D=1+(1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10)

D=1+(1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)

D=1+(1/4-1/10)

D=1+3/5

D=8/5

27 tháng 5 2022

Quãng sông AB dài là :

    8 giờ 24 phú x 10 = 84 (km)

    Vận tốc cua ca nô khi xuôi dòng là :

    10 + 2 = 12 (km/giờ )

    Thời gian ca nô đi xuôi dòng là :

    84 : 2 = 7 (giờ )

         Đáp số : 7 giờ 

29 tháng 5 2022

= -( 1/1.2 +1/2.3 +1/3.4 + 1/4.5 +1/5.6 + 1/6.7 +1/7.8+ 1/8.9 +1/9.10)

= -( 1-1/2 + 1/2-1/3+1/3 -1/4+.....+1/9-1/10)

= -(1-1/10)

= - 9/10