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5 tháng 5 2019
Sửa đề : \(\frac{3}{7\cdot9}+\frac{3}{9\cdot11}+\frac{3}{11\cdot13}+...+\frac{3}{57\cdot59}\)
\(=\frac{3}{2}\left[\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+...+\frac{2}{57\cdot59}\right]\)
\(=\frac{3}{2}\left[\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{57}-\frac{1}{59}\right]\)
\(=\frac{3}{2}\left[\frac{1}{7}-\frac{1}{59}\right]=\frac{78}{413}\)
P/S : Thi gặp dạng này thì dễ rồi -_-
5 tháng 5 2019
\(\frac{3}{7.9}+\frac{3}{9.11}+\frac{3}{11.13}+...+\frac{3}{57.59}\)
\(=\frac{3}{2}.\left(\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+...+\frac{2}{57.59}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+...+\frac{1}{57}-\frac{1}{59}\right)\)
\(=\frac{3}{2}.\left[\frac{1}{7}+\left(\frac{1}{9}-\frac{1}{9}\right)+\left(\frac{1}{11}-\frac{1}{11}\right)+\left(\frac{1}{13}-\frac{1}{13}\right)+...+\left(\frac{1}{57}-\frac{1}{57}\right)-\frac{1}{59}\right]\)
\(=\frac{3}{2}.\left[\frac{1}{7}-\frac{1}{59}\right]\)
\(=\frac{3}{2}.\frac{52}{413}=\frac{78}{413}\)
13 tháng 3 2022
\(\dfrac{x}{2}+\dfrac{3x}{5}-\dfrac{6}{5}=3\Leftrightarrow\dfrac{11x}{10}=3+\dfrac{6}{5}=\dfrac{21}{5}\)
\(\Rightarrow11x=42\Leftrightarrow x=\dfrac{42}{11}\)
VN
13 tháng 3 2022
\(\frac{1}{2}\)x + \(\frac{3}{5}\)( x - 2 ) = 3
\(\frac{1}{2}\)x + \(\frac{3}{5}\) x - \(\frac{3}{5}\). 2 = 3
x \((\)\(\frac{1}{2}\)+ \(\frac{3}{5}\) \()\)- \(\frac{6}{5}\) = 3
x . \(\frac{11}{10}\) - \(\frac{6}{5}\) = 3
x . \(\frac{11}{10}\) = 3 + \(\frac{6}{5}\) = \(\frac{21}{5}\)
x = \(\frac{21}{5}\) : \(\frac{11}{10}\) = \(\frac{42}{11}\)
NẾU CÓ GÌ SAI SÓT MONG BẠN THÔNG CẢM
20 tháng 12 2015
ai làm chi tiết cho mik đi mik tick người đó 5 li-ke
17 tháng 7 2015
Số đó có dạng \(27k+15\) (k \(\in\) N).
Ta có \(27k+15=3.9k+3.5=3.\left(9k+5\right)\) chia hết cho 3.
\(27k+15=9.3k+9+6=9.\left(3k+1\right)+6\) không chia hết cho 9.
29 tháng 9 2016
\(x^2+xy+y^2+1=\left(x^2+xy+\frac{y^2}{4}\right)+\frac{3y^2}{4}+1=\left(x+\frac{y}{2}\right)^2+\frac{3y^2}{4}+1>0\)
30 tháng 9 2016
\(\frac{1}{9}+\frac{8}{9}=\frac{1+8}{9}=\frac{9}{9}=1\)
\(\frac{1}{12}+\frac{2}{12}+\frac{6}{12}+\frac{3}{12}=\frac{1+2+6+3}{12}=\frac{12}{12}=1\)
Chúc bạn học tốt !!
JL
30 tháng 9 2016
\(\frac{1}{9}\)+\(\frac{8}{9}\)=\(\frac{1+8}{9}\)=\(\frac{9}{9}\)=\(1\)
\(\frac{1}{12}\)+\(\frac{2}{12}\)+\(\frac{6}{12}\)+\(\frac{3}{12}\)=\(\frac{1+2+6+3}{12}\)=\(\frac{12}{12}\)=\(1\)
5 tháng 7 2017
đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{18.19.20}\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}\left(\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{380}\right)=\frac{189}{760}\)
Đặt \(B=\frac{3}{1.2}+\frac{3}{2.3}+...+\frac{3}{19.20}=\frac{3}{1}-\frac{3}{2}+\frac{3}{2}-\frac{3}{3}+...+\frac{3}{19}-\frac{3}{20}\)
\(=3-\frac{3}{20}=\frac{57}{20}\)
\(D=A-B=\frac{189}{760}-\frac{57}{20}=-\frac{1977}{760}\)
5 tháng 7 2017
Gọi \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{18.19.20}\)là A
\(\frac{3}{1.2}-\frac{3}{2.3}-...-\frac{3}{19.20}\)là B
\(A=\left[\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{18.19}-\frac{1}{19.20}\right)\right]\)
\(A=\left[\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\right]\)
\(A=\left[\frac{1}{2}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}\right)\right]\)
\(A=\left[\frac{1}{2}.\left(1-\frac{1}{20}\right)\right]\)
\(A=\frac{1}{2}.\frac{19}{20}\)
\(A=\frac{19}{40}\)
\(B=\frac{3}{1.2}-\frac{3}{2.3}-...-\frac{3}{19.20}\)
\(B=\left(\frac{3}{1.2}+\frac{3}{2.3}+...+\frac{3}{19.20}\right)\)
\(B=\left[3.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\right)\right]\)
\(B=\left[3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{2}{3}+...+\frac{1}{19}-\frac{1}{20}\right)\right]\)
\(B=\left[3.\left(\frac{19}{20}\right)\right]\)
\(B=\frac{57}{20}\)
Vậy A - B = \(\frac{19}{40}-\frac{57}{20}\)
\(=-\frac{95}{40}=-\frac{19}{8}\)
Nếu đúng thì k nha
d) \(x+\dfrac{3}{4}=\dfrac{36}{144}.\dfrac{-12}{9}\)
\(\Rightarrow x+\dfrac{3}{4}=\dfrac{-1}{3}\)
\(\Rightarrow x=\dfrac{-1}{3}-\dfrac{3}{4}\)
\(\Rightarrow x=\dfrac{-4}{12}-\dfrac{9}{12}\)
\(\Rightarrow x=\dfrac{-13}{12}\)
e)
\(\dfrac{8}{23}.\dfrac{46}{24}=\dfrac{1}{3}.x\)
\(\Rightarrow\dfrac{1}{3}.x=\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{2}{3}:\dfrac{1}{3}\)
\(\Rightarrow x=\dfrac{2}{3}.3\)
\(\Rightarrow x=2\)
f)
\(\dfrac{1}{5}:x=\dfrac{1}{5}-\dfrac{1}{7}\)
\(\dfrac{1}{5}:x=\dfrac{7}{35}-\dfrac{5}{35}\)
\(\dfrac{1}{5}:x=\dfrac{2}{35}\)
\(\Rightarrow x=\dfrac{1}{5}:\dfrac{2}{35}\)
\(\Rightarrow x=\dfrac{1}{5}.\dfrac{35}{2}\)
\(\Rightarrow x=\dfrac{7}{2}\)
f) 1/5 : x = 1/5 - 1/7
1/5 : x = 2/35
x = 1/5 : 2/35
x = 7/2
e) x + 3/4 = 36/144 . -12/9
x + 3/4 = -1/3
x = -1/3 - 3/4
x = -13/12