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\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{72}+\dfrac{1}{90}\)
\(=\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{1}{3}-\dfrac{1}{10}\)
`=7/30`
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)
\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}\)
\(=\dfrac{9}{10}\)
* Bạn tham khảo nhé *
1212 ++ 1616 ++ 112112 ++ 120120 ++ 130130 ++ 142142 ++ 156156
== 11×211×2 ++ 12×312×3 ++ 13×413×4 ++ 14×514×5 ++ 15×615×6 ++ 16×716×7 ++ 17×817×8
== 1111 −− 1212 ++ 1212 −− 1313 ++ 1313 −− 1414 ++ 1414 −− 1515 ++ 1515 −− 1616 ++ 1616 −− 1717 ++ 1717 −− 1818
== 1111 −− 1818
== 8888 −− 1818
== 78
\(\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}-\frac{1}{3\cdot4}-\frac{1}{4\cdot5}-\frac{1}{5\cdot6}\)
\(=\frac{1}{1}-\frac{1}{2}-\frac{1}{2}-\frac{1}{3}-\frac{1}{3}-\frac{1}{4}-\frac{1}{4}-\frac{1}{5}-\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{1}-\frac{1}{6}=\frac{5}{6}\)
NHỚ K MK NHA. CHÚC BẠN HỌC TỐT
1/2 - 1/6 - 1/12 - 1/20 - 1/30
=1/1x2 - 1/2x3- 1/3x4 - 1/4x5 - 1/5x6
=1-1/2 + 1/2-1/3 + 1/3-1/4 + 1/4-1/5 +1/5-1/6
=1-1/6
=5/6
\((\frac{1}{2}+\frac{1}{4}+\frac{1}{6}) \)x \((\frac{36}{9}-\frac{12}{9}:\frac{1}{3}) \)
\(= (\frac{1}{2}+\frac{1}{4}+\frac{1}{6}) \) x \((\frac{36}{9}-\frac{36}{9})\)
\( = (\frac{1}{2}+\frac{1}{4}+\frac{1}{6}) \) x \(0\)
\(= 0\)
Bài 1 :
a) Hai phân số có chung tử số thì ta so sánh mẫu nếu mẫu lớn hơn thì phân số đó bé hơn
Áp dụng vào đó ta có : 71 < 72 => 15/71 > 15/72
b) Ta có : 21/42 = 1/2 = 23/46
Áp dụng câu a ta có : 46 > 45 => 21/42 < 23/45
c) Ta có : 47/45 = 1 + 2/45 ; 48/46 = 1 + 2/46
Vì 2/45 > 2/46 => 47/45 > 48/46
d) Ta có : 1 - 13/25 = 12/25
1/3 = 12/36
Vì 12/25 > 12/36 => 13/25 > 3/7
Bài 2 :
D = 1/2 + 1/6 + 1/12 + 1/20 + ... + 1/110
D = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + .... + 1/10.11
D = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + .... + 1/10 - 1/11
D = 1 - 1/11
D = 10/11
\(\frac{1}{2}+\frac{2}{4}+\frac{3}{6}+\frac{4}{8}+\frac{5}{10}+\frac{6}{12}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=6\times\frac{1}{2}=3\)
\(\frac{8}{14}+\frac{5}{12}+\frac{6}{14}+\frac{8}{12}-\frac{1}{12}\)
\(=\left(\frac{8}{14}+\frac{6}{14}\right)+\left(\frac{5}{12}+\frac{8}{12}-\frac{1}{12}\right)\)
\(=1+1=2\)
\(\frac{8}{14}+\frac{5}{12}+\frac{6}{14}+\frac{8}{12}-\frac{1}{12}\)
\(=\left(\frac{8}{14}+\frac{6}{14}\right)+\left(\frac{5}{12}+\frac{8}{12}-\frac{1}{12}\right)\)
\(=1+1=2\)
~ Hok tốt ~
3/4 x 7/12 + 3/4 x 1/6 + 3/4 x 1/4
=3/4 x (7/12 + 1/6 + 1/4)
=3/4 x (7/12 + 2/12 + 3/12)
=3/4 x 1
=3/4
Chúc học tốt~
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+....+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{1}-\frac{1}{11}\)
\(=\frac{10}{11}\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\)\(+\frac{1}{110}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...\) \(+\frac{1}{9\cdot10}\)\(+\frac{1}{10\cdot11}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\)\(\frac{1}{5}\)\(+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\)\(+\frac{1}{10}-\frac{1}{11}\)
\(=1-\frac{1}{11}\)
\(=\frac{10}{11}\)
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{90}\\ =\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{90}\\ =\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}\right)+\dfrac{1}{90}\\ =\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\right)+\dfrac{1}{90}\\ =\left(1-\dfrac{1}{5}\right)+\dfrac{1}{90}\\ =\left(\dfrac{5}{5}-\dfrac{1}{5}\right)+\dfrac{1}{90}\\ =\dfrac{4}{5}+\dfrac{1}{90}\\ =\dfrac{72}{90}+\dfrac{1}{90}=\dfrac{73}{90}\)
1/2 + 1/6 + 1/12 + 1/20 + 1/90
= 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) + 1/90
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/90
= 1 - 1/5 + 1/90
= 4/5 - 1/90
= 71/90