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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

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 :

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1 tháng 5 2017

\(\dfrac{2x}{4}+\dfrac{2x}{28}+\dfrac{2x}{70}+...+\dfrac{2x}{418}=\dfrac{14}{11}\)

\(\dfrac{2x}{1.4}+\dfrac{2x}{4.7}+\dfrac{2x}{7.10}+\dfrac{2x}{10.13}+...+\dfrac{2x}{19.22}=\dfrac{14}{11}\)

Ta có công thức : \(\dfrac{a}{b.c}=\dfrac{a}{c-b}.\left(\dfrac{1}{b}-\dfrac{1}{c}\right)\)

Dựa vào công thức ta có :

\(\dfrac{2x}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{19}-\dfrac{1}{22}\right)=\dfrac{14}{11}\)

\(\dfrac{2x}{3}.\left(1-\dfrac{1}{22}\right)=\dfrac{14}{11}\)

\(\Leftrightarrow\) \(\dfrac{2x}{3}.\left(\dfrac{21}{22}\right)=\dfrac{14}{11}\)

\(\Rightarrow\) \(\dfrac{2x}{3}=\dfrac{14}{11}:\dfrac{21}{22}=\dfrac{4}{3}\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=2\)

Ai thấy đúng thì ủng hộ nha !!!!

banhqua

2 tháng 5 2017

Ai thấy đúng ủng hộ với

banhqua

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

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

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

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

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

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

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

7 tháng 2 2023

`1/15+1/35+1/63+1/99+1/143`

`=1/[3.5]+1/[5.7]+1/[7.9]+1/[9.11]+1/[11.13]`

`=1/2(2/[3.5]+2/[5.7]+2/[7.9]+2/[9.11]+2/[11.13])`

`=1/2.(1/3-1/5+1/5-1/7+...+1/11-1/13)`

`=1/2.(1/3-1/13)`

`=1/2 . 10/39`

`=5/39`