\(\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+...+\dfrac{1}{152}\)

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30 tháng 8 2017

A = \(\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+...+\dfrac{1}{152}\)

=> \(\dfrac{3}{2}\)A = \(\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+...+\dfrac{3}{304}\)

= \(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{16.19}\)

= \(1-\dfrac{1}{19}=\dfrac{18}{19}\)

=> A = \(\dfrac{18}{19}:\dfrac{3}{2}=\dfrac{12}{19}\)

30 tháng 8 2017

\(A=\dfrac{1}{2}+\dfrac{1}{14}+.......+\dfrac{1}{152}\)

\(\Leftrightarrow A=\dfrac{3}{2}\left(\dfrac{3}{4}+\dfrac{3}{28}+...........+\dfrac{3}{304}\right)\)

\(\Leftrightarrow A=\dfrac{3}{2}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+.........+\dfrac{3}{16.19}\right)\)

\(\Leftrightarrow A=\dfrac{3}{2}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+......+\dfrac{1}{16}-\dfrac{1}{19}\right)\)

\(\Leftrightarrow A=\dfrac{3}{2}\left(1-\dfrac{1}{19}\right)\)

\(\Leftrightarrow A=\dfrac{3}{2}.\dfrac{18}{19}=\dfrac{12}{19}\)

15 tháng 5 2017

\(C=\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\)

\(=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\)

\(=\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+\dfrac{2}{10.13}+\dfrac{2}{13.16}+\dfrac{2}{16.19}\)

\(=\dfrac{2}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19}\right)\)

\(=\dfrac{2}{3}.\left(1-\dfrac{1}{19}\right)\)

\(=\dfrac{2}{3}.\dfrac{18}{19}=\dfrac{12}{19}\)

4 tháng 5 2018

Giải sách bà i tập Toán 6 | Giải bà i tập Sách bà i tập Toán 6

18 tháng 4 2017

Ta có :

\(C=\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\)

\(C=\dfrac{1}{1.2}+\dfrac{1}{2.7}+\dfrac{1}{7.5}+\dfrac{1}{5.13}+\dfrac{1}{13.16}+\dfrac{1}{16.19}\)

\(C=\dfrac{2}{3}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+\dfrac{3}{13.16}+\dfrac{3}{16.19}\right)\)

\(C=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19}\right)\)

\(C=\dfrac{2}{3}\left(1-\dfrac{1}{19}\right)\)

\(C=\dfrac{2}{3}.\dfrac{18}{19}=\dfrac{12}{19}\)

~ Học tốt ~

18 tháng 4 2017

C=2/4+2/28+2/70+2/130+2/208+2/304

C=2/1.4+2/4.7+2/7.10+2/10.13+2/13.16+2/16.19

C=2/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16+3/16.19)

C=2/3(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16+1/16-1/19)

C=2/3(1-1/19)

C=2/3.18/19=12/19

15 tháng 4 2017

\(C=\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\)

\(=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\)

\(=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+\dfrac{2}{7\cdot10}+\dfrac{2}{10\cdot13}+\dfrac{2}{13\cdot16}+\dfrac{2}{16\cdot19}\)

\(=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{16\cdot19}\right)\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{16}-\dfrac{1}{19}\right)\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{19}\right)=\dfrac{2}{3}\cdot\dfrac{18}{19}=\dfrac{12}{19}\)

15 tháng 4 2017

Ta có :

\(C=\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\)

\(\Rightarrow C=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\)

\(=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4\cdot+4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}+\dfrac{3}{16\cdot19}\right)\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{16}-\dfrac{1}{19}\right)\)

\(=\dfrac{2}{3}\left(1-\dfrac{1}{19}\right)\)

\(=\dfrac{2}{3}\cdot\dfrac{18}{19}\)

\(=\dfrac{12}{19}\)

12 tháng 3 2017

1. Tính nhanh:

\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)

\(=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)

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

\(=\dfrac{1}{2}-\dfrac{1}{8}\)

\(=\dfrac{3}{8}\)

12 tháng 3 2017

2. Tính nhanh

Đặt \(A\) = \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

\(A\) \(=\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}\)

\(2A=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\)

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

\(2A=\dfrac{10}{39}\)

\(A=\dfrac{10}{39}:2\)

\(A=\dfrac{5}{39}\)

25 tháng 3 2018


=1/1.2+1/2.7+1/7.5+1/5.13+1/13.8+1/8.19=2/1.4+2/4.7+2/7.10+2/10.13+2/13.16+2/16.19(ca tu va mau cung nhan them 2 gia tri khong doi)=2/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16+3/16.19)=2/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/101/13+1/13-1/16+1/16-1/19)=2/3.18/19=12/19

1 tháng 8 2017

c) E = \(\dfrac{4116-14}{10290-35}\) và K = \(\dfrac{2929-101}{2.1919+404}\)

E = \(\dfrac{4116-14}{10290-35}\)

E = \(\dfrac{14.\left(294-1\right)}{35.\left(294-1\right)}\)

E = \(\dfrac{14}{35}\)

K = \(\dfrac{2929-101}{2.1919+404}\)

K = \(\dfrac{101.\left(29-1\right)}{101.\left(38+4\right)}\)

K = \(\dfrac{29-1}{34+8}\)

K = \(\dfrac{28}{42}\) = \(\dfrac{2}{3}\)

Ta có : E = \(\dfrac{14}{35}\) và K = \(\dfrac{2}{3}\)

\(\dfrac{14}{35}\) = \(\dfrac{42}{105}\)

\(\dfrac{2}{3}\) = \(\dfrac{70}{105}\)

Vậy E < K

Các câu còn lại tương tự

27 tháng 3 2017

A=\(\dfrac{2}{7}+\dfrac{-3}{8}+\dfrac{11}{7}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{5}{-3}\)

A=\(\left(\dfrac{2}{7}+\dfrac{11}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{3}+\dfrac{5}{-3}\right)+\dfrac{-3}{8}\)

A=\(2+\dfrac{-4}{3}+\dfrac{-3}{8}\)

A=\(\dfrac{7}{24}\)

B=\(\dfrac{3}{17}+\dfrac{-5}{13}+\dfrac{-18}{35}+\dfrac{14}{17}+\dfrac{17}{-35}+\dfrac{-8}{13}\)

B=\(\left(\dfrac{3}{17}+\dfrac{14}{17}\right)+\left(\dfrac{-18}{35}+\dfrac{17}{-35}\right)+\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)\)

B=\(\dfrac{17}{17}+\dfrac{-35}{35}+\dfrac{-13}{13}\)

B=\(1+\left(-1\right)+\left(-1\right)=-1\)

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

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

C=0+\(\dfrac{2}{3}=\dfrac{2}{3}\)

D=\(\left(\dfrac{-1}{6}+\dfrac{5}{-12}\right)+\dfrac{7}{12}\)

D=\(\dfrac{-1}{6}+\dfrac{5}{-12}+\dfrac{7}{12}\)

D=\(\dfrac{-2}{12}+\dfrac{-5}{12}+\dfrac{7}{12}=\left(\dfrac{-2}{12}+\dfrac{-5}{12}\right)+\dfrac{7}{12}\)

D=\(\dfrac{-7}{12}+\dfrac{7}{12}=0\)

23 tháng 7 2017

Các bạn không cần trả lời câu hỏi trên của mik vì mik đã hiểu rồi nha . Cho nên đừng trả lời ! OKleuleu

23 tháng 7 2017

Mình khuyen bạn phải suy nghĩ kĩ bài trước khi đăng lên nhé!!hum

4 tháng 4 2017

a, \(2-\dfrac{14}{x}=\dfrac{-22}{3}\)

\(\dfrac{14}{x}=2-\dfrac{-22}{3}=\dfrac{28}{3}\)

\(\dfrac{14}{x}=\dfrac{28}{3}\)

=> \(x.28=14.3\)

\(x.28=42\)

\(x=42:28\)

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

b, \(\left(\dfrac{2x}{5}+1\right):\left(-7\right)=\dfrac{1}{35}\)

\(\dfrac{2x}{5}+1=\dfrac{1}{35}.\left(-7\right)=-\dfrac{1}{5}\)

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

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

=> \(2x=-6\)

\(x=-6:2=-3\)

4 tháng 4 2017

a)

\(2-\dfrac{14}{x}=-\dfrac{22}{3}\)

\(\Rightarrow\dfrac{14}{x}=2-\dfrac{-22}{3}=\dfrac{28}{3}\)

\(\Rightarrow x=\dfrac{14.3}{28}=\dfrac{3}{2}=1,5\)

b)

\(\left(\dfrac{2x}{5}+1\right):\left(-7\right)=\dfrac{1}{35}\)

\(\Rightarrow\dfrac{2x}{5}+1=\dfrac{1}{35}.\left(-7\right)\)

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

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

Hay \(\dfrac{2x}{5}=-\dfrac{6}{5}\)

\(\Rightarrow2x=-6\)

\(\Rightarrow x=-\dfrac{6}{2}=-3\)

Chúc bạn học tốt!ok