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\(VT=91\left(\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+...+\dfrac{1}{88\cdot91}\right)\)

\(=\dfrac{91}{3}\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{88\cdot91}\right)\)

\(=\dfrac{91}{3}\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{88}-\dfrac{1}{91}\right)\)

\(=\dfrac{91}{3}\cdot\dfrac{90}{91}=30\)

14 tháng 5 2019

\(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.10}+...+\frac{91}{88.91}\)

\(=91.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{88.91}\right)\)

\(=91.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{88}-\frac{1}{91}\right)\)

\(=91.\left(\frac{1}{1}-\frac{1}{91}\right)\)

\(=91.\frac{90}{91}=\frac{91.90}{91}\)

\(=90\)

14 tháng 5 2019

#)Giải :

= 91 - 91/4 + 91/4 - 91/7 + 91/7 - 91/10 + ... + 91/88 - 91/91

= 91 - 1 

= 90 

     #~Will~be~Pens~#

27 tháng 4 2018

     \(\frac{91}{1.4}+\frac{91}{4.7}+\frac{9}{7.10}+...+\frac{91}{88.91}\)

\(\frac{91}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{88.91}\right)\)

\(\frac{91}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{88}-\frac{1}{91}\right)\)

\(\frac{91}{3}.\frac{90}{91}=30\) (đfcm)

14 tháng 5 2019

ai nhanh mk tích cho nào cảm ơn

17 tháng 8 2020

a) \(\frac{91}{1.4}+\frac{91}{4.7}+...+\frac{91}{88.91}=\frac{91}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{88.91}\right)\)

\(=\frac{91}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{88}-\frac{1}{91}\right)=\frac{91}{3}\left(1-\frac{1}{91}\right)=\frac{91}{3}.\frac{90}{91}=30\left(\text{đpcm}\right)\)

a: \(\dfrac{-13}{40}< \dfrac{-12}{40}\)

\(\dfrac{-5}{6}>\dfrac{-91}{104}\)

17 tháng 7 2023

Sao bn giống BT mình thế ?:)

9: \(=\dfrac{47}{51}\cdot\dfrac{17}{94}-\dfrac{47}{51}\cdot\dfrac{53}{91}-\dfrac{53}{91}\cdot\dfrac{91}{53}+\dfrac{53}{91}\cdot\dfrac{47}{51}\)

\(=\dfrac{1}{6}-1=-\dfrac{5}{6}\)

10: \(=\dfrac{13}{19}\cdot\dfrac{19}{26}-\dfrac{13}{19}\cdot\dfrac{71}{43}+\dfrac{71}{43}\cdot\dfrac{13}{19}-\dfrac{71}{43}\cdot\dfrac{86}{71}\)

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

5 tháng 2 2023

bạn giải chi tiết đi

 

 

14 tháng 5 2021

`16/803+38+(-16/803)`
`=16/803-16/803+38`
`=0+38=38`

14 tháng 5 2021

`100/91+310-9/91`
`=100/91-9/91+310`
`=1+310=311`

1 tháng 7 2018

\(\dfrac{1909-x}{91}+\dfrac{1907-x}{93}+\dfrac{1905-x}{95}+\dfrac{1903}{97}+4=0\) ( Sửa đề)

\(\dfrac{1909-x}{91}+1+\dfrac{1907-x}{93}+1+\dfrac{1905-x}{95}+1+\dfrac{1903}{97}+1=0\)\(\dfrac{2000-x}{91}+\dfrac{2000-x}{93}+\dfrac{2000-x}{95}+\dfrac{2000-x}{97}=0\)

\(\left(2000-x\right)\left(\dfrac{1}{91}+\dfrac{1}{93}+\dfrac{1}{95}+\dfrac{1}{97}\right)=0\)

Do : \(\dfrac{1}{91}+\dfrac{1}{93}+\dfrac{1}{95}+\dfrac{1}{97}>0\)

\(\text{⇔}2000-x=0\)

\(\text{⇔}x=2000\)

Vậy ,....

29 tháng 12 2019

Where 4

16 tháng 11 2018

1/

a) ta có \(\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{97.100}=\dfrac{1}{3}.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{97.100}\right)\)

\(=\dfrac{1}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(=\dfrac{1}{3}.\dfrac{99}{100}=\dfrac{33}{100}\)

\(\dfrac{33}{100}=\dfrac{0,33x}{2009}\)

\(\dfrac{33}{100}=\dfrac{0,33}{2009}.x\Rightarrow x=\dfrac{33}{100}:\dfrac{0,33}{2009}=2009\)

16 tháng 11 2018

b,1 + 1/3 + 1/6 + 1/10 + ... + 2/x(x+1)=1 1991/1993

2 + 2/6 + 2/12 + 2/20 + ... + 2/x(x+1) = 3984/1993

2.(1/1.2 + 1/2.3 + 1/3.4 + ... + 1/x(x+1) = 3984/1993

2.(1 − 1/2 + 1/2 − 1/3 + ... + 1/x − 1/x+1)=3984/1993

2.(1 − 1/x+1) = 3984/1993

1 − 1/x + 1= 3984/1993 :2

1 − 1/x+1 = 1992/1993

1/x+1 = 1 − 1992/1993

1/x+1=1/1993

<=>x+1 = 1993

<=>x+1=1993

<=> x+1=1993

<=> x = 1993-1

<=> x = 1992