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\(=\dfrac{1}{8}\left(1+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}\right)\)

\(=\dfrac{1}{8}\cdot2\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\right)\)

\(=\dfrac{1}{4}\cdot\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{6}-\dfrac{1}{7}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{6}{7}=\dfrac{3}{14}\)

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

Y
3 tháng 3 2019

\(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}\)

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(A=1-\dfrac{1}{100}=\dfrac{99}{100}\)

\(B=\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+..+\dfrac{1}{195}\) ( là 195 ms đúng ! )

\(B=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{13\cdot15}\)

\(B=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)\)

\(B=\dfrac{1}{2}\left(1-\dfrac{1}{15}\right)=\dfrac{1}{2}\cdot\dfrac{14}{15}=\dfrac{7}{15}\)

\(C=\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+...+\dfrac{1}{98\cdot100}\)

Rồi làm tương tự cân b nha!

\(D=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{32}+\dfrac{1}{32}-\dfrac{1}{57}\)

\(+\dfrac{1}{57}-\dfrac{1}{87}\)

\(D=\dfrac{1}{3}-\dfrac{1}{87}=\dfrac{28}{87}\)

3 tháng 3 2019

Cảm ơn bạn nhìu nha!!!yeuvuihihi

17 tháng 4 2017

a) ; b) ; c) ; d) ; e) ; g) .

1 tháng 5 2018

Giải bà i 69 trang 36 SGK Toán 6 Tập 2 | Giải toán lá»p 6

14 tháng 3 2017

đây là tính nhanh à nếu tính bình thường thì tính may tính là ra

14 tháng 3 2017

a) 17/23 . 8/16 . 23/17. (-80) . 3/4

= (17/23 . 23/17) . (8/16 . 3/4) . (-80)

= 1 . 3/8 . (-80)

= 3/8 . (-80)

= -30

b) 5/11 . 18/29 - 5/11 . 8/29 + 5/11 . 19/29

= 5/11 . (18/29 - 8/29 + 19/29)

= 5/11 . 1

= 5/11

c)(13/23 + 1313/2323 - 131313/232323).(1/3+1/4 -7/12)

= (13/23 + 1313/2323 - 131313/232323).0

= 0

d) 12/2x2 . 22/2x3 . 32/3x4 . 42/4x5 . 52/5x6 . 62/6x7 . 72/7x8 . 82/8x9 . 92/9x10

= 1/2 . 2/3 . 3/4 . 4/5 . 5/6 . 6/7 . 7/8 . 8/9 .9/10

= 1/10

Khó nhìn quá. Bạn thông cảm nhé! vui

20 tháng 3 2017

a , \(\left(\dfrac{-2}{3}+1\dfrac{1}{4}-\dfrac{1}{6}\right):\dfrac{-24}{10}\)

=\(\left(\dfrac{-2}{3}+\dfrac{5}{4}-\dfrac{1}{6}\right):\dfrac{-12}{5}\)

=\(\left(\dfrac{-8}{12}+\dfrac{15}{12}-\dfrac{2}{12}\right)\cdot\dfrac{-5}{12}\)

=\(\dfrac{5}{12}\cdot\dfrac{-5}{12}=\dfrac{-25}{144}\)

b , \(\dfrac{13}{15}\cdot0,25\cdot3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right)1\dfrac{23}{24}\)

=\(\dfrac{13}{15}\cdot\dfrac{1}{4}\cdot3+\left(\dfrac{8}{15}-\dfrac{79}{60}\right)\cdot\dfrac{57}{24}\)

=\(\dfrac{13}{20}-\dfrac{47}{60}\cdot\dfrac{57}{24}\)

=\(\dfrac{13}{20}-\dfrac{893}{480}=\dfrac{312}{480}-\dfrac{893}{480}=\dfrac{-581}{480}\)

c , \(\left(\dfrac{12}{32}+\dfrac{5}{-20}-\dfrac{10}{24}\right):\dfrac{2}{3}\)

=\(\left(\dfrac{180}{480}-\dfrac{120}{480}-\dfrac{200}{480}\right)\cdot\dfrac{3}{2}\)

= \(\dfrac{-7}{24}\cdot\dfrac{3}{2}=\dfrac{-7}{16}\)

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

=\(\dfrac{9}{2}:\left(\dfrac{5}{2}-\dfrac{15}{4}\right)-\dfrac{1}{2}\)

=\(\dfrac{9}{2}:\dfrac{-5}{4}-\dfrac{1}{2}=\dfrac{9}{2}\cdot\dfrac{-4}{5}-\dfrac{1}{2}=\dfrac{-18}{5}-\dfrac{1}{2}=\dfrac{-41}{10}\)

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

=\(\dfrac{-5}{2}:\dfrac{1}{4}=\dfrac{-5}{2}\cdot4=-10\)

17 tháng 4 2017

Lời giải:

Giải bài 159 trang 64 SGK Toán 6 Tập 2 | Giải toán lớp 6Giải bài 159 trang 64 SGK Toán 6 Tập 2 | Giải toán lớp 6

17 tháng 4 2017

a) \(\dfrac{1}{6};\dfrac{1}{3};\dfrac{1}{2};...\)

\(\Rightarrow\dfrac{1}{6};\dfrac{2}{6};\dfrac{3}{6};...\)

Dãy có quy luật tăng dần lên 1 đơn vị ở tử số

\(\Rightarrow\) Số tiếp theo của dãy là: \(\dfrac{4}{6}\)

b) \(\dfrac{1}{8};\dfrac{5}{24};\dfrac{7}{24};...\)

\(\Rightarrow\dfrac{3}{24};\dfrac{5}{24};\dfrac{7}{24};...\)

Dãy có quy luật tăng dần lên 2 đơn vị ở tử số

\(\Rightarrow\) Số tiếp theo của dãy là: \(\dfrac{9}{24}\)

c) \(\dfrac{1}{5};\dfrac{1}{4};\dfrac{1}{3};...\)

\(\dfrac{4}{20};\dfrac{5}{20};\dfrac{6}{20};...\)

Dãy có quy luật tăng dần lên 1 đơn vị ở tử số

\(\Rightarrow\) Số tiếp theo của dãy là: \(\dfrac{7}{20}\)

d) \(\dfrac{4}{15};\dfrac{3}{10};\dfrac{1}{3};...\)

\(\Rightarrow\dfrac{8}{30};\dfrac{9}{30};\dfrac{11}{30};...\)

Dãy có quy luật tăng dần lên 1 đơn vị ở tử số

\(\Rightarrow\) Số tiếp theo của dãy là: \(\dfrac{12}{30}\)

a: \(\Leftrightarrow\dfrac{8}{5}+\dfrac{2}{5}\cdot x=\dfrac{16}{5}\)

=>2/5x=8/5

=>x=4

b: \(\Leftrightarrow\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{26}+...+\dfrac{1}{39}-\dfrac{1}{40}\right)\cdot120+\dfrac{1}{3}x=-4\)

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

=>1/3x=-6

=>x=-18

c: =>2|x-1/3|=0,24-4/5=-0,56<0

5 tháng 4 2017

1) \(-\dfrac{5}{9}+1\dfrac{5}{9}\cdot\left(\dfrac{3}{4}-\dfrac{2}{5}\right):7^2\\ =-\dfrac{5}{9}+\dfrac{14}{9}\cdot\dfrac{7}{20}\cdot\dfrac{1}{49}\\ =-\dfrac{5}{9}+\dfrac{1}{90}=\dfrac{-49}{90}\)

2) \(1\dfrac{13}{15}\cdot0,75-\left(\dfrac{104}{195}+25\%\right)\cdot\dfrac{24}{47}-3\dfrac{12}{13}:3\\ =\dfrac{28}{15}\cdot\dfrac{3}{4}-\left(\dfrac{8}{15}+\dfrac{1}{4}\right)\cdot\dfrac{24}{47}-\dfrac{51}{13}\cdot\dfrac{1}{3}\\ =\dfrac{7}{5}-\dfrac{47}{60}\cdot\dfrac{24}{47}-\dfrac{17}{13}\\ =\dfrac{7}{5}-\dfrac{2}{5}-\dfrac{17}{13}\\ =-\dfrac{4}{13}\)

3) \(1\dfrac{13}{15}\cdot\left(0,5\right)^2\cdot3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\\ =\dfrac{28}{15}\cdot\dfrac{1}{4}\cdot3+\left(\dfrac{8}{15}-\dfrac{79}{60}\right):\dfrac{47}{24}\\ =\dfrac{7}{5}-\dfrac{47}{60}\cdot\dfrac{24}{47}\\ =\dfrac{7}{5}-\dfrac{2}{5}\\ =1\)

Tìm x : 1) \(60\%x+0,4x+x:3=2\\ \Leftrightarrow\dfrac{3}{5}x+\dfrac{2}{5}x+\dfrac{1}{3}x=2\\ \Leftrightarrow\dfrac{4}{3}x=2\\ \Leftrightarrow x=\dfrac{3}{2}\)

5 tháng 4 2017

Nốt nè bn

\(-2x-\dfrac{-3}{5}:\left(0,5\right)^2=-1\dfrac{1}{4}\\ \Leftrightarrow-2x+\dfrac{3}{5}:\dfrac{1}{4}=-\dfrac{5}{4}\\ \Leftrightarrow-2x+\dfrac{12}{5}=-\dfrac{5}{4}\\ \Leftrightarrow-2x=-\dfrac{73}{20}\\ x=-\dfrac{73}{40}\)

\(\left(\dfrac{2}{3}-x\right):\dfrac{3}{4}=\dfrac{1}{5}\\ \Leftrightarrow\dfrac{2}{3}-x=\dfrac{1}{5}\cdot\dfrac{3}{4}\\ \Leftrightarrow\dfrac{2}{3}-x=\dfrac{3}{20}\\ \Leftrightarrow x=\dfrac{2}{3}-\dfrac{3}{20}\\ \Leftrightarrow x=\dfrac{31}{60}\)

17 tháng 4 2017

a) \(\dfrac{1}{3}+\dfrac{3}{8}-\dfrac{7}{12}\)

\(=\dfrac{17}{24}-\dfrac{7}{12}\)

\(=\dfrac{1}{8}\)

b) \(\dfrac{-3}{14}+\dfrac{5}{8}-\dfrac{1}{2}\)

\(=\dfrac{23}{56}-\dfrac{1}{2}\)

\(=\dfrac{-5}{56}\)

c) \(\dfrac{1}{4}-\dfrac{2}{3}-\dfrac{11}{18}\)

\(=\dfrac{-5}{12}-\dfrac{11}{18}\)

\(=\dfrac{-37}{36}\)

d) \(\dfrac{1}{4}+\dfrac{5}{12}-\dfrac{1}{13}-\dfrac{7}{8}\)

\(=\dfrac{2}{3}-\dfrac{1}{13}-\dfrac{7}{8}\)

\(=\dfrac{23}{39}-\dfrac{7}{8}\)

\(=\dfrac{-89}{312}\)