\(\dfrac{1}{3}\)+\(\dfrac{1}{6}\)+\(\dfr...">
K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

21 tháng 4 2017

1/3+1/6+1/10+...+2/x(x+1)=998/1000

2/6+2/12+2/20+...+2/x(x+1)=998/1000

2[1/2.3+1/3.4+1/4.5+...+1/x(x+1)]=998/1000

2[1/2-1/3+1/3-1/4+1/4-1/5+...+1/x+1/(x+1)]=998/1000

2.[1/2-1/(x+1)]=998/1000

1/2-1/(x+1)=499/1000

1/(x+1)=1/2-499/1000

1/(x+1)=1/1000

=> x=999

21 tháng 4 2017

tốc độ ánh sáng hà trời

2 tháng 5 2017

a) \(\left(2x-3\right)\left(6-2x\right)=0\)

\(\circledast\)TH1: \(2x-3=0\\ 2x=0+3\\ 2x=3\\ x=\dfrac{3}{2}\)

\(\circledast\)TH2: \(6-2x=0\\ 2x=6-0\\ 2x=6\\ x=\dfrac{6}{2}=3\)

Vậy \(x\in\left\{\dfrac{3}{2};3\right\}\).

b) \(\dfrac{1}{3}x+\dfrac{2}{5}\left(x-1\right)=0\)

\(\dfrac{1}{3}x=0-\dfrac{2}{5}\left(x-1\right)\)

\(\dfrac{1}{3}x=-\dfrac{2}{5}\left(x-1\right)\)

\(-\dfrac{2}{5}-\dfrac{1}{3}=-x\left(x-1\right)\)

\(-\dfrac{11}{15}=-x\left(x-1\right)\)

\(\Rightarrow x=1.491631652\)

Vậy \(x=1.491631652\)

c) \(\left(3x-1\right)\left(-\dfrac{1}{2}x+5\right)=0\)

\(\circledast\)TH1: \(3x-1=0\\ 3x=0+1\\ 3x=1\\ x=\dfrac{1}{3}\)

\(\circledast\)TH2: \(-\dfrac{1}{2}x+5=0\\ -\dfrac{1}{2}x=0-5\\ -\dfrac{1}{2}x=-5\\ x=-5:-\dfrac{1}{2}\\ x=10\)

Vậy \(x\in\left\{\dfrac{1}{3};10\right\}\).

d) \(\dfrac{x}{5}=\dfrac{2}{3}\\ x=\dfrac{5\cdot2}{3}\\ x=\dfrac{10}{3}\)

Vậy \(x=\dfrac{10}{3}\).

e) \(\dfrac{x}{3}-\dfrac{1}{2}=\dfrac{1}{5}\\ \)

\(\dfrac{x}{3}=\dfrac{1}{5}+\dfrac{1}{2}\)

\(\dfrac{x}{3}=\dfrac{7}{10}\)

\(x=\dfrac{3\cdot7}{10}\)

\(x=\dfrac{21}{10}\)

Vậy \(x=\dfrac{21}{10}\).

f) \(\dfrac{x}{5}-\dfrac{1}{2}=\dfrac{6}{10}\)

\(\dfrac{x}{5}=\dfrac{6}{10}+\dfrac{1}{2}\)

\(\dfrac{x}{5}=\dfrac{11}{10}\)

\(x=\dfrac{5\cdot11}{10}\)

\(x=\dfrac{55}{10}=\dfrac{11}{2}\)

Vậy \(x=\dfrac{11}{2}\).

g) \(\dfrac{x+3}{15}=\dfrac{1}{3}\\ x+3=\dfrac{15}{3}=5\\ x=5-3\\ x=2\)

Vậy \(x=2\).

h) \(\dfrac{x-12}{4}=\dfrac{1}{2}\\ x-12=\dfrac{4}{2}=2\\ x=2+12\\ x=14\)

Vậy \(x=14\).

Tính nhanh theo mẫu: Mẫu: \(B=\left(1+\dfrac{1}{3}\right)\)x \(\left(1+\dfrac{1}{8}\right)\)x \(\left(1+\dfrac{1}{15}\right)\)x \(\left(1+\dfrac{1}{24}\right)\)x ..... x \(\left(1+\dfrac{1}{120}\right)\)x \(\left(1+\dfrac{1}{413}\right)\) \(B=\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\)x \(\left(\dfrac{8}{8}+\dfrac{1}{8}\right)\)x \(\left(\dfrac{15}{15}+\dfrac{1}{15}\right)\)x \(\left(\dfrac{24}{24}+\dfrac{1}{24}\right)\)x........x\(\left(\dfrac{120}{120}+\dfrac{1}{120}\right)\)x...
Đọc tiếp

Tính nhanh theo mẫu:

Mẫu: \(B=\left(1+\dfrac{1}{3}\right)\)x \(\left(1+\dfrac{1}{8}\right)\)x \(\left(1+\dfrac{1}{15}\right)\)x \(\left(1+\dfrac{1}{24}\right)\)x ..... x \(\left(1+\dfrac{1}{120}\right)\)x \(\left(1+\dfrac{1}{413}\right)\)

\(B=\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\)x \(\left(\dfrac{8}{8}+\dfrac{1}{8}\right)\)x \(\left(\dfrac{15}{15}+\dfrac{1}{15}\right)\)x \(\left(\dfrac{24}{24}+\dfrac{1}{24}\right)\)x........x\(\left(\dfrac{120}{120}+\dfrac{1}{120}\right)\)x \(\left(\dfrac{143}{143}+\dfrac{1}{143}\right)\)

\(B=\dfrac{4}{3}\)x\(\dfrac{9}{8}\)x\(\dfrac{16}{15}\)x\(\dfrac{25}{24}\)x.......x\(\dfrac{121}{120}\)x \(\dfrac{144}{143}\)

\(B=\dfrac{2x2}{1x3}\)x\(\dfrac{3x3}{2x4}\)x\(\dfrac{4x4}{3x5}\)x\(\dfrac{5x5}{4x6}\)x.......x\(\dfrac{11x11}{10x12}\)x\(\dfrac{12x12}{13x11}\)

\(B=\dfrac{2x3x4x5x......x10x11x12}{1x2x3x......x10x11x12}\)x \(\dfrac{2x3x4x5x....x11x12}{3x4x5x6x......x12x13}\)

B= \(\dfrac{12}{1}\)x\(\dfrac{2}{13}\)

B=\(\dfrac{24}{13}\)

Câu hỏi:

\(B=\left(1+\dfrac{1}{8}\right)\)x\(\left(1+\dfrac{1}{15}\right)\)x\(\left(1+\dfrac{1}{24}\right)\)x..... x \(\left(1+\dfrac{1}{440}\right)\)x \(\left(1+\dfrac{1}{483}\right)\)

3
24 tháng 6 2017

\(B=\left(1+\dfrac{1}{8}\right)\left(1+\dfrac{1}{15}\right)\left(1+\dfrac{1}{24}\right).....\left(1+\dfrac{1}{440}\right)\left(1+\dfrac{1}{483}\right)\)

\(B=\dfrac{9}{8}.\dfrac{16}{15}.\dfrac{25}{24}.....\dfrac{441}{440}.\dfrac{484}{483}\)

\(B=\dfrac{9.16.25.....441.484}{8.15.24.....440.483}\)

\(B=\dfrac{3.3.4.4.5.5.....21.21.22.22}{2.4.3.5.4.6.....20.22.21.23}\)

\(B=\dfrac{3.4.5.....21.22}{2.3.4.....20.21}.\dfrac{3.4.5.....21.22}{4.5.6.....22.23}\)

\(B=11.\dfrac{3}{23}=\dfrac{33}{23}\)

24 tháng 6 2017

B = \(\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.\dfrac{25}{24}...\dfrac{121}{120}.\dfrac{144}{143}\)

B = \(\dfrac{4.9.16.25...121.144}{3.8.15.24....120.143}\)

B = \(\dfrac{2.2.3.3.4.4.5.5...11.11.12.12}{1.3.2.4.3.5.4.6...10.12.11.13}\)

B = \(\dfrac{2.3.4.5...11.12}{1.2.3.4.5...10.11}.\dfrac{2.3.4.5...11.12}{3.4.5.6.7...12.13}\)

B = 12 . \(\dfrac{2}{13}\)

B = \(\dfrac{24}{13}\)

13 tháng 3 2017

Các bạn giúp tớ với, sáng mai mình học rồi.hihihihihahavui

13 tháng 3 2017

a)\(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+\dfrac{1}{11\cdot14}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{101}{1540}\)

\(\Leftrightarrow\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)=\dfrac{101}{1540}\)

\(\Leftrightarrow\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)=\dfrac{101}{1540}\)

\(\Leftrightarrow\dfrac{1}{5}-\dfrac{1}{x+3}=\dfrac{303}{1540}\)\(\Leftrightarrow\dfrac{1}{x+3}=\dfrac{1}{308}\)

\(\Leftrightarrow x+3=308\Leftrightarrow x=305\)

6 tháng 5 2018

\(\dfrac{1}{7}=\dfrac{8}{-x}\)=> \(-x=56\)

=> \(x=56\)

2) => 18x = 18

=> x = 1

3) \(\dfrac{-4}{3}+x=\dfrac{-11}{6}\)

=> \(x=\dfrac{-11}{6}+\dfrac{4}{3}\)

=> \(x=\dfrac{-1}{2}\)

4) 45%.x =\(\dfrac{3}{5}\)

=> \(x=\dfrac{3}{5}:\dfrac{9}{20}\)

=> \(x=\dfrac{4}{3}\)

2 tháng 5 2017

a) \(-\dfrac{2}{3}x+\dfrac{1}{5}=\dfrac{3}{10}\)

\(-\dfrac{2}{3}x=\dfrac{3}{10}-\dfrac{1}{5}\)

\(-\dfrac{2}{3}x=\dfrac{1}{10}\)

x=\(\dfrac{1}{10}:-\dfrac{2}{3}\)

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

Vậy \(x=-\dfrac{3}{20}\).

b) \(\dfrac{1}{3}+\dfrac{2}{3}:x=-7\)

\(\dfrac{2}{3}:x=-7-\dfrac{1}{3}\)

\(\dfrac{2}{3}:x=-\dfrac{22}{3}\)

\(x=\dfrac{2}{3}:-\dfrac{22}{3}\)

\(x=-\dfrac{1}{11}\)

Vậy \(x=-\dfrac{1}{11}\).

c) \(60\%x=\dfrac{1}{3}\cdot6\dfrac{1}{3}\)

\(60\%x=\dfrac{19}{9}\)

\(\dfrac{3}{5}x=\dfrac{19}{9}\)

\(x=\dfrac{19}{9}:\dfrac{3}{5}\)

\(x=\dfrac{95}{27}\)

Vậy \(x=\dfrac{95}{27}\).

d) \(\left(\dfrac{2}{3}-x\right):\dfrac{3}{4}=\dfrac{1}{5}\)

\(\dfrac{2}{3}-x=\dfrac{1}{5}\cdot\dfrac{3}{4}\)

\(\dfrac{2}{3}-x=\dfrac{3}{20}\)

\(x=\dfrac{2}{3}-\dfrac{3}{20}\)

\(x=\dfrac{31}{60}\)

Vậy \(x=\dfrac{31}{60}\).

e) \(-2x-\dfrac{-3}{5}:\left(-0.5\right)^2=-1\dfrac{1}{4}\)

\(-2x-\dfrac{-12}{5}=-1\dfrac{1}{4}\)

\(-2x=-1\dfrac{1}{4}+\dfrac{-12}{5}\)

\(-2x=-\dfrac{73}{20}\)

\(x=-\dfrac{73}{20}:\left(-2\right)\)

\(x=\dfrac{73}{40}\)

Vậy \(x=\dfrac{73}{40}\).

30 tháng 6 2017

\(1+\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{x\left(x+2\right)}=1\dfrac{2009}{2011}\)

\(\Rightarrow\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{x\left(x+2\right)}=\dfrac{4020}{4022}\)

\(\Rightarrow\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{x\left(x+2\right)}=\dfrac{4020}{4022}\)

\(\Rightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{4020}{4022}\)

\(\Rightarrow1-\dfrac{1}{x+2}=\dfrac{4020}{4022}\)

\(\Rightarrow\dfrac{1}{x+2}=\dfrac{1}{2011}\)

\(\Rightarrow x+2=2011\Rightarrow x=2009\)

Vậy x = 2009

14 tháng 2 2018

\(\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2000}{2002}\)

=> \(2.\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2000}{2002}\)

=> 2.\(\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2000}{2002}\)

=> 2.\(\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2000}{2002}\)

=> 2.\(\left(\dfrac{1}{2}-\dfrac{1}{x+1}\right)=\dfrac{2000}{2002}\)

=> 1-\(\dfrac{2}{x+1}-\dfrac{2000}{2002}=0\)

=> \(1-\dfrac{2000}{2002}=\dfrac{2}{x+1}\)

=> \(\dfrac{2}{2002}=\dfrac{2}{x+1}\)

=> x+1=2002

=> x=2002-1=2001

5 tháng 8 2018

a, (x + 1) + (x + 4) + ... + (x + 28) = 155

x + 1 + x + 4 + ... + x + 28 = 155

(x + x + x + ... + x) + (1 + 4 + ... + 28) = 155

x . 10 + 145 = 155

x . 10 = 155 - 145

x . 10 = 10

x = 10 : 10

x = 1