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= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ............. + 1/99 - 1/100
= 1 - 1/100
= 99/100
\(B=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{20}\right)\)
\(B=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{19}{20}\)
\(B=\frac{1}{20}\)
\(4\frac{2}{7}.3=\left(4+\frac{2}{7}\right).3=4.3+\frac{2}{7}.3=12+\frac{6}{7}=12\frac{6}{7}\)
Cách này nhanh hơn nhiều đúng không
\(B=-\frac{2}{17}+\frac{15}{23}+-\frac{15}{17}+\frac{4}{19}+\frac{8}{23}\)
\(B=\left(-\frac{2}{17}+-\frac{15}{17}\right)+\left(\frac{15}{23}+\frac{8}{23}\right)+\frac{4}{19}\)
\(B=\left(-1\right)+1+\frac{4}{19}\)
\(B=0+\frac{4}{9}=\frac{4}{9}\)
\(C=-\frac{1}{2}+\frac{3}{21}+-\frac{2}{6}+-\frac{5}{30}\)
\(C=-\frac{1}{2}+\frac{1}{7}+-\frac{1}{3}+-\frac{1}{6}\)
\(C=\left(-\frac{1}{2}+-\frac{1}{3}+-\frac{1}{6}\right)+\frac{1}{7}\)
\(C=\left(-1\right)+\frac{1}{7}\)
\(C=-\frac{6}{7}\)
Ủng hộ tk Đúng nhé ! ^^
B= -2 + 15 + (-15) + 4 + 8
17 23 17 19 23
B= [(-2) + (-15)] + [15 + 8] + 4
17 17 23 23 19
B= -1 +1+ 4 vậy B=4
19 19
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{72}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)
\(=\frac{1}{2}-\frac{1}{9}=\frac{9}{18}-\frac{2}{18}=\frac{7}{18}\)
dễ mà phân tích các mẫu ra là các tích của 2 số gần liên tiếp rồi áp dụng phân số ai cập thui
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)
\(A=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(A=\frac{1}{5}-\frac{1}{12}=\frac{7}{60}\)
A = 18:26+(-5):27+(-22):86+12:39+(-32):43 = 9:13+(-5):27+(-11):43+4:13+(-32):43 = (9:13+4:13)+[(-11):43+(-32):43]+(-5):27 = 1+(-1)+5:27 = -5:27
B =(-10):12+8:15+(-19):56+3:(-18)+28:60 = (-5):6+8:15+(-19):56+1:(-6)+7:15 = [(-5):6+1:(-6)]+(8:15+7:15)+(-19):56 = (-1)+1+(-19):56 = (-19) :56
a/ \(A=\frac{1}{6}+\frac{1}{12}+.........+\frac{1}{56}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{7.8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{4}\)
b/ \(B=\frac{5}{11.16}+\frac{5}{16.21}+........+\frac{5}{61.66}\)
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+........+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}\)
\(=\frac{5}{66}\)
a) \(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(A=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
b) \(B=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(B=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(B=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6
= 1 - 1/6
= 5/6
1/2 + 1/6 + 1/12 + 1/20 + 1/30
= 30/60 + 10/60 + 5/60 + 3/60 + 2/60
= 50/60 = 5/6
Có ai đồng tình ý kiến với mình không