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c; 17\(\dfrac{2}{31}\) - (\(\dfrac{15}{17}\) + 6\(\dfrac{2}{31}\))
= 17 + \(\dfrac{2}{31}\) - \(\dfrac{15}{17}\) - 6 - \(\dfrac{2}{31}\)
= (17 - 6) - \(\dfrac{15}{17}\) + (\(\dfrac{2}{31}\) - \(\dfrac{2}{31}\))
= 11 - \(\dfrac{15}{17}\)+ 0
= \(\dfrac{172}{17}\)
b; 130\(\dfrac{25}{28}\) + 120\(\dfrac{17}{35}\)
= 130 + \(\dfrac{25}{28}\) + 120 + \(\dfrac{17}{35}\)
= (130 + 120) + (\(\dfrac{25}{28}\) + \(\dfrac{17}{35}\))
= 250 + (\(\dfrac{125}{140}\) + \(\dfrac{68}{140}\))
= 250 + \(\dfrac{193}{140}\)
= 250\(\dfrac{193}{140}\)
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{19.20}\)
\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20}\right)\)
\(=2.\left(1-\frac{1}{20}\right)\)
\(=2.\frac{19}{20}=\frac{19}{10}\)
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{19.20}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{1}-\frac{1}{20}\)
\(=\frac{19}{20}\)
A = 1 + 2 + 3 + ... + 2018 (có 2018 số )
= (2018 + 1) . 2018 : 2 = 2037171
B = 1 + 3 + 5 + ... + 2017(có 1009 số )
= (2017 + 1) . 1009 : 2 = 1018081
C = 2 + 4 + 6 + ... + 2018 (Có 1009 số )
= (2018 + 2) x 1009 : 2 = 1019090
D = 72 . 153 + 27.153 + 153
= (72 + 27 + 1) . 153
= 100 . 153 = 15300
Đặt A = 1.2 + 2.3 + 3.4 + ... + 98.99
A = 1/3 . ( 1.2.3 + 2.3.3 + 3.4.3 + ... + 98.99.3)
A = 1/3 . [ 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... + 98.99.(100-97)
A = 1/3 . ( 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 98.99.100 - 97.98.99)
A = 1/3 . [(1.2.3 + 2.3.4 + 3.4.5 + ... + 98.99.100) - ( 0.1.2 + 1.2.3 + 2.3.4 + ... + 97.98.99)]
A = 1/3 . ( 98.99.100 - 0.1.2)
A = 1/3 .98.99.100
A = 323400
Ta có: 323400x/26950 = 12/6/7 : 3/2
12x = 14 × 2/3
12x = 28/3
x = 28/3 : 12
x = 28/3 × 1/12 = 7/9
Vậy x = 7/9
A= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2018.2019}\)
A= 1 - \(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{2018}-\frac{1}{2019}\)
A= 1 - \(\frac{1}{2019}\)
A= \(\frac{2018}{2019}\)
\(\frac{1313}{1212}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\)\(\frac{1}{5.6}\)
\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{6}\)
\(\Leftrightarrow\frac{13}{12}:x=\frac{5}{6}\)
\(\Leftrightarrow x=\frac{13}{12}:\frac{5}{6}\)
\(\Leftrightarrow x=\frac{13}{10}\)
Vậy \(x=\frac{13}{10}\)
~~~~~Hok tốt ~~~~~
a,\(\frac{1313}{1212}\div x=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(\frac{13}{12}\div x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\frac{13}{12}\div x=1-\frac{1}{6}\)
\(\frac{13}{12}\div x=\frac{5}{6}\)
\(x=\frac{13}{12}\div\frac{5}{6}\)
\(x=\frac{13}{12}\times\frac{6}{5}\)
\(x=\frac{13}{10}\)
Chúc bạn hok tốt !
\(\frac{1313}{1212}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\)\(\frac{1}{5.6}\)
\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{6}\)
\(\Leftrightarrow\frac{13}{12}:x=\frac{5}{6}\)
\(\Leftrightarrow x=\frac{13}{12}:\frac{5}{6}\)
\(\Leftrightarrow x=\frac{13}{10}\)
Hok tốt
Ta có: A = 1.2 + 2.3 + 3.4 + 4.5 +.....+ 98.99
=> 3A = 1.2.(3 - 0) + 2.3.(4 - 1) + ..... +98.99.(100 - 97)
=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 98.99.100
=> 3A = 98.99.100
=> A = 98.99.100 / 3
=> A = 323400