11/19 . 12/29 - 11/19 . 2/29 + 11/19 . 19/29
(Tính hợp lý nếu có thể)
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NT
2
29 tháng 6 2016
= 1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90
= 1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90
= 9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
= 9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)]
= 9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
= 9 – (1 – 1/10) = 9 – 9/10 = 81/10
29 tháng 6 2016
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+...+\frac{89}{90}\)
\(=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+...+\left(1-\frac{1}{90}\right)\)
\(=\left(1-\frac{1}{1.2}\right)+\left(1-\frac{1}{2.3}\right)+\left(1-\frac{1}{3.4}\right)+...+\left(1-\frac{1}{9.10}\right)\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
9 số 1
\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=9-\left(1-\frac{1}{10}\right)\)
\(=9-\frac{9}{10}\)
\(=\frac{81}{10}\)
Ủng hộ mk nha ^-^
ND
1
12 tháng 8 2016
1/2 + 5/6 + 11/12 + 19/20 + 29/30 +. . . 9701 + / 9702 + 9899/9900 = 1/2 + (1-1 / 6) + (1-1 / 12) + (1-1 / 20) + (1-1 / 30) + ...... + (1 -1/9702) + (1-1 / 9900) = 1/2 + [1 - (1 / 2-1 / 3)] + [1 - (1 / 3-1 / 4)] + [1- ( 1 / 4-1 / 5)] + [1 - (1 / 5-1 / 6)] + ...... + [1- (1 / 98-1 / 99)] + [1 - (1 / 99-1 / 100)] * 100 + 1 = 1 / 2-1 / 2 + 1 / 3-1 / 3 + 1 / 4-1 / 4 + 1 / 5-1 / 5 + 1 / 6-1 / 6 + ... ... 1 / 98-1 / 98 + 1 / 99-1 / 99 + 1/100 + 1 = 100/100 = 100 và 1/100
H9
HT.Phong (9A5)
CTVHS
13 tháng 7 2023
a) \(\dfrac{25}{37}\times\dfrac{18}{29}+\dfrac{18}{29}\times\dfrac{12}{37}\)
\(=\dfrac{18}{29}\times\left(\dfrac{25}{37}+\dfrac{12}{37}\right)\)
\(=\dfrac{18}{29}\times\dfrac{37}{37}\)
\(=\dfrac{18}{29}\times1\)
\(=\dfrac{18}{29}\)
b) \(\dfrac{31}{85}\times\dfrac{11}{19}+\dfrac{31}{85}\times\dfrac{12}{19}-\dfrac{42}{19}\times\dfrac{31}{85}\)
\(=\dfrac{31}{85}\times\left(\dfrac{11}{19}+\dfrac{12}{19}-\dfrac{42}{19}\right)\)
\(=\dfrac{31}{85}\times\dfrac{-19}{19}\)
\(=\dfrac{31}{85}\times-1\)
\(=-\dfrac{31}{85}\)
c) \(\dfrac{16}{53}:\dfrac{17}{9}-\dfrac{16}{53}:\dfrac{17}{8}\)
\(=\dfrac{16}{53}:\left(\dfrac{9}{17}-\dfrac{8}{17}\right)\)
\(=\dfrac{16}{53}:\dfrac{1}{17}\)
\(=\dfrac{16}{901}\)
c) \(\dfrac{1}{5}\times\dfrac{12}{31}\times\dfrac{4}{3}+\dfrac{19}{31}\times\dfrac{4}{15}\)
\(=\dfrac{4}{15}\times\dfrac{12}{31}+\dfrac{19}{31}\times\dfrac{4}{15}\)
\(=\dfrac{4}{15}\times\left(\dfrac{12}{31}+\dfrac{19}{31}\right)\)
\(=\dfrac{4}{15}\times\dfrac{31}{31}\)
\(=\dfrac{4}{15}\times1\)
\(=\dfrac{4}{15}\)
13 tháng 7 2023
a: =18/29*(25/37+12/37)
=18/29
b: =31/85(11/19+12/19-42/19)
=-31/85
c; =16/53(9/17+8/17)=16/53
d: =4/15(12/31+19/31)=4/15
CV
1
AH
Akai Haruma
Giáo viên
21 tháng 7 2021
Lời giải:
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}\)
\(=5-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)
\(=5-\left(\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{5-4}{4\times 5}+\frac{6-5}{5\times 6}\right)\)
\(=5-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(=5-\left(1-\frac{1}{6}\right)=5-\frac{5}{6}=\frac{25}{6}\)
15 tháng 4 2021
10/29+11/29+12/29+...+19/29
=10+11+12+13+14+15+=16+17+18+19/29
=145/29
9 tháng 1 2017
5/11 . 18/29 - 8/11 . 5/29 + 5/29 . 19/11
=5/11x(5/29+13/29)-8/11 . 5/29 + 5/29 . 19/11
=5/11x5/29+13/29x5/11-8/11x5/29+5/29x19/11
=(5/11x5/29+13/29x5/11)-(8/11x5/29-5/29x19/11)
=5/11x(5/29+13/29)-5/29x(8/11-19/11)
=5/11x18/29-5/29x(-1)
=90/319-(-5/29)=5/11
KT
15 tháng 10 2018
\(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{38}{5}\)
\(\dfrac{11}{19}.\dfrac{12}{29}-\dfrac{11}{19}.\dfrac{2}{29}+\dfrac{11}{19}.\dfrac{19}{29}\)
\(=\dfrac{11}{19}.\left(\dfrac{12}{29}-\dfrac{2}{29}+\dfrac{19}{29}\right)\)
\(=\dfrac{11}{19}.1\)
\(=\dfrac{11}{19}\)