\(C=70.\left(\dfrac{131313}{565656}+\dfrac{131313}{727272}+\dfrac{131313}{9909090}\right)\)
\(B=\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+......+\dfrac{1}{ }64.69\)
\(A=\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+....+\dfrac{2}{97.100}\)
70.\(\left(\dfrac{131313}{565656}+\dfrac{131313}{727272}+\dfrac{131313}{909090}\right)\)
B=70.
B=70.
B=70.=39
nhớ tick cho mình nhe
C =\(70\left(\dfrac{131313}{565656}+\dfrac{131313}{727272}+\dfrac{131313}{909090}\right)\)
\(C=70.\left(131313.\left(\dfrac{1}{565656}+\dfrac{1}{727272}+\dfrac{1}{909090}\right)\right)\)
\(C=70.\left(131313.\dfrac{1}{235690}\right)\)
\(C=70.\dfrac{39}{70}\)
\(C=39\)
\(\dfrac{2}{3.x}-70\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{99999}\right)\)= -5
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[13\left(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}\right)\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-\dfrac{780}{11}:\left[\dfrac{13}{2}\cdot\dfrac{8}{33}\right]=-5\)
\(\Leftrightarrow\dfrac{2}{3x}-45=-5\)
=>2/3x=40
=>3x=1/20
hay x=1/60
Tìm x, biết :
\(\dfrac{2}{3}x-70\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\)
\(\dfrac{2}{3}x-70\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left(\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right)=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:13\left(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}\right)=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:13.\dfrac{4}{33}=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\dfrac{52}{33}=-5\\ \Rightarrow\dfrac{2}{3}x-45=-5\\ \Rightarrow\dfrac{2}{3}x=40\\ \Rightarrow x=60\)
Tìm x biết :
\(\dfrac{3}{2}\)x - \(70\dfrac{10}{11}\) : \(\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\left[\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right]=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\right]=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\left[\dfrac{13}{2}\left(\dfrac{1}{3}-\dfrac{1}{11}\right)\right]=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}-\dfrac{780}{11}:\dfrac{52}{33}=-5\)
\(\Leftrightarrow x\cdot\dfrac{3}{2}=40\)
hay x=40:3/2=80/3
Tính:
B = [-2008. 57 + 1004. (-86) : [32. 74] + 16. (-48)
C = 75. (2 - 128) - 128. (-75)
D = \(\left(1.\dfrac{1}{2}\right).\left(1.\dfrac{1}{3}\right).\left(1.\dfrac{1}{4}\right)...\left(1.\dfrac{1}{2018}\right)\)
E = \(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+\dfrac{1}{64.69}+\dfrac{1}{69}.74\)
b: \(C=75\left(2-128+128\right)=75\cdot2=150\)
e: \(E=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{69\cdot74}\right)\)
\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{69}-\dfrac{1}{74}\right)\)
\(=\dfrac{1}{5}\cdot\dfrac{70}{74}=\dfrac{14}{74}=\dfrac{7}{37}\)
A=\(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right)\dfrac{1-3-5-7-...-49}{89}\)
Ta có: \(A=\left(\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+\dfrac{1}{14\cdot19}+...+\dfrac{1}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+\dfrac{5}{14\cdot19}+...+\dfrac{5}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{1}{4}-\dfrac{1}{49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{1}{5}\cdot\left(\dfrac{49-4}{4\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{1}{5}\cdot\dfrac{45}{196}\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{9}{196}\cdot\dfrac{1-3-5-7-...-49}{89}\)
\(\Leftrightarrow A=\dfrac{9}{196}\cdot\dfrac{-623}{89}=-\dfrac{9}{28}\)
\(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right)\dfrac{1-3-5-7-...-49}{89}\)
thực hiện phép tính
Đặt \(A=\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}\)
\(=\dfrac{1}{5}\left(\dfrac{5}{4.9}+\dfrac{5}{9.14}+\dfrac{5}{14.19}+...+\dfrac{5}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}\)
\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{49}\right).\dfrac{1-3-5-7-...-49}{89}\)
\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{49}\right).\dfrac{1-3-5-7-...-49}{89}\)
\(=\dfrac{9}{196}.\dfrac{1-3-5-7-...-49}{89}\)
Đặt \(B=1-3-5-7-..-49\)
\(=1-\left(3+5+7+...+49\right)\)
\(=1-\left\{\left(49+3\right).\left[\left(49-3\right):2+1\right]:2\right\}\)
\(=1-624\)
\(=-623\)
\(\Rightarrow\dfrac{9}{196}.\left(\dfrac{-623}{89}\right)=-\dfrac{9}{28}\)
Vậy: \(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}=-\dfrac{9}{28}\)
Xét \(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right)\)
=\(\dfrac{1}{5}\left(\dfrac{5}{4.9}+\dfrac{5}{9.14}+\dfrac{5}{14.19}+...+\dfrac{5}{44.49}\right)\)
=\(\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{49}\right)\)
=\(\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{49}\right)\)
=\(\dfrac{1}{5}.\dfrac{45}{196}\)
=\(\dfrac{9}{196}\)
Xét \(\dfrac{1-3-5-7-..-49}{89}\)
=\(\dfrac{1-\left(3+5+7+...+49\right)}{89}\)
CT tính sl số hạng (số cuối - số đầu ):2+1
số lượng số hạn của dãy 3+5+7+...+49 là (49-3):2+1=24
Áp dụng CT tính tổng số hạng dãy số cách đều Tổng = [ (số đầu + số cuối) x Số lượng số hạng ] : 2
=> tổng = [(3+49).24]:2=624
=>\(\dfrac{1-624}{89}\)
=\(\dfrac{-623}{89}\)
=-7
từ đó ta có \(\dfrac{9}{196}.\left(-7\right)=\dfrac{-9}{28}\)
Tính :
c) C = \(\dfrac{2}{4.7}-\dfrac{3}{5.9}+\dfrac{2}{7.10}-\dfrac{3}{9.13}+...+\dfrac{2}{301.304}-\dfrac{3}{401.405}\)
d) D = \(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\left(\dfrac{1-3-5-7-...-49}{89}\right)\)