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\(\dfrac{1}{4}-\dfrac{1}{3}+\dfrac{5}{12}\\ =\dfrac{3}{12}-\dfrac{4}{12}+\dfrac{5}{12}\\ =\dfrac{3-4+5}{12}\\ =\dfrac{4}{12}\\ =\dfrac{1}{3}\)
\(\left(\frac{10}{99}+\frac{11}{199}-\frac{12}{299}\right)\times\left(\frac{1}{2}-\frac{1}{3}+-\frac{1}{6}\right)\)
\(=\left(\frac{10}{99}+\frac{11}{199}-\frac{12}{299}\right)\times\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\left(\frac{10}{99}+\frac{11}{199}-\frac{12}{299}\right)\times\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
\(=\left(\frac{10}{99}+\frac{11}{199}-\frac{12}{299}\right)\times0\)
\(=0\)
A = - [-806 - (-791) + 2012] - (806 - 1791)
A = 806 - 791 + 2012 - 806 + 1791
A = (806 - 806) + (1791 - 791)
A = 1000
B = 9 - (119).34 + 119.(-77) - (-119).11
B = 9 - 119(34 + 77 - 11)
B = 9 - 119.100
B = 9 - 11900
B = - 11891
\(\text{ta có: }\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{3.4}=\frac{1}{3}-\frac{1}{4}\)
\(\frac{1}{4.5}=\frac{1}{4}-\frac{1}{5}\)
...........................
\(\frac{1}{39.40}=\frac{1}{39}-\frac{1}{40}\)
Đồng nhất 2 vế ta có:
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{39}-\frac{1}{40}=\frac{1}{2}-\frac{1}{40}=\frac{19}{40}\)
Ta có :
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{39.40}\)
\(=\)\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{39}-\frac{1}{40}\)
\(=\)\(\frac{1}{2}-\frac{1}{40}\)
\(=\)\(\frac{20}{40}-\frac{1}{40}\)
\(=\)\(\frac{19}{40}\)
Vậy \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{39.40}=\frac{19}{40}\)
12-12+11+10-9+8-7+5-4+3+2-1
=-(12+12-11-10)-(9-8+7-5)+(4-3-2+1)
=(-3)-3+0
=(-6)
Chúc bn học tốt
ô mai gót TAO.........................Đ......É....O ......H...I....Ể....U........OK!
\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right)...\left(1-\frac{1}{190}\right)\)
\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}...\frac{189}{190}\)
\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{378}{380}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{18.21}{19.20}\)
\(=\frac{1.2.3...18}{2.3.4...19}.\frac{4.5.6...21}{3.4.5...20}\)
\(=\frac{1}{19}.\frac{21}{3}\)
\(=\frac{1}{19}.7=\frac{7}{19}\)
\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right)...\left(1-\frac{1}{190}\right)\)
\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}....\frac{189}{190}\)
\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}....\frac{378}{380}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}....\frac{18.21}{19.20}\)
\(=\frac{1.2.3....18}{2.3.4....19}.\frac{4.5.6...21}{3.4.5....20}\)
\(=\frac{1}{19}.\frac{21}{3}\)
\(=\frac{1}{19}.7=\frac{7}{19}\)
Ủng hộ mk nha !!! ^_^