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TT
21 tháng 5 2017
Lưu An
\(A=\dfrac{1}{19}+\left(\dfrac{9}{19\cdot29}+\dfrac{9}{29\cdot39}+...+\dfrac{9}{1999\cdot2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+\dfrac{10}{29\cdot39}+...+\dfrac{10}{1999\cdot2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}\cdot\dfrac{1990}{38171}\)
\(A=\dfrac{1}{19}+\dfrac{1791}{38171}\)
\(A=\dfrac{200}{2009}\)
21 tháng 5 2017
B=1/19+(9/19.29+9/29.39+...+9/1999.2009)
B=1/19+9/10+(10/19.29+10/29.39+.....+10/1999.2009
B=1/19+9/10+(1/19-1/29+1/29-1/39+....+1/1999-1/2009)
B=1/19+9/10+(1/19-1/2009)
B=1/19+9/10.1990/38171
B=1/19+1791/38171
B=200/2009
Vậy B= 200/2009
NL
0
31 tháng 12 2022
a)= 2021.2021-2020.(2021+1)
= 2021.(2020+1)-2020.(2021+1)
= (2021.2020)+2021-(2020.2021)-2020
= 1
31 tháng 12 2022
b) B= (1+2-3-4)+(5+6-7-8)+(9+10-11-12)...........+(2017+2018-2019-2020)+2021
B= -4+(-4)+....................(-4)+2021
B= -4x505+2021
B= -2020 + 2021
B = 1
NN
2
19 tháng 9 2018
A=5.230318-22.320.227
=229.318.(5.2-32)
=229.318.1
B=5.29.219.319-7.219.318
=5.228.319-7.219.318
=228.318.(5.3-7.2)
=228.318.1
vậy A:B=(229.318):(228.318)=2
HN
12 tháng 3 2019
\(A=\frac{-3}{7}+\frac{14}{23}+\frac{-14}{17}+\frac{9}{23}-\frac{5}{19}\)
\(\Rightarrow A=-\frac{3}{7}+\left(\frac{14}{23}+\frac{9}{23}\right)-\frac{14}{17}-\frac{5}{19}\)
\(\Rightarrow A=\frac{-3}{7}+1-\frac{14}{17}-\frac{5}{19}\)
Tính nốt nhé
\(B=\frac{5}{9}.\frac{7}{13}.\frac{5}{9}.\frac{9}{13}.\left(-\frac{5}{13}\right).\frac{3}{9}\)
Tương tự câu A
14 tháng 7 2023
\(A=5.4^{15}.9^9-4.3^{20}.8^9\)
\(A=5.2^{30}.3^{27}-2^2.3^{20}.2^{27}=2^{29}.3^{20}.\left(5.2.3^7-1\right)\)
\(A=2^{29}.3^{20}.\left(21870-1\right)=2^{29}.3^{20}.21869\)
11 tháng 8 2023
2:
a: =4+3/8+5+2/3
=9+3/8+2/3
=216/24+9/24+16/24
=216/24+25/24
=241/24
b; =2+3/8+1+1/4+3+6/7
=6+3/8+1/4+6/7
=6+5/8+6/7
=419/56
c: \(=2+\dfrac{3}{8}-1-\dfrac{1}{4}+5+\dfrac{1}{3}\)
=6+3/8-1/4+1/3
=6+1/8+1/3
=6+11/24
=155/24
d: \(=3+\dfrac{5}{6}+6\cdot\dfrac{13}{6}\)
=3+13+5/6
=16+5/6
=101/6
e: =3+1/2+4+5/7-5-5/14
=3+4-5+1/2+5/7-5/14
=2+7/14+10/14-5/14
=2+12/14
=2+6/7=20/7
f: =9/2+1/2:11/2
=9/2+1/11
=99/22+2/22=101/22
HT
7 tháng 8 2015
B = \(\frac{1}{10.9}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405}\)
B = \(\frac{2}{10.18}+\frac{2}{18.26}+\frac{2}{26.34}+...+\frac{2}{802.810}\)
B = \(\frac{1}{4}.\left(\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+\frac{1}{26}-\frac{1}{34}+...+\frac{1}{802}-\frac{1}{810}\right)\)
B = \(\frac{1}{4}.\left(\frac{1}{10}-\frac{1}{810}\right)=\frac{1}{4}.\frac{8}{81}\)
B = \(\frac{2}{81}\)
Đề đúng phải là: \(B=\frac{9}{9\cdot19}+\frac{9}{19\cdot29}+\frac{9}{29\cdot39}+...+\frac{9}{2009\cdot2019}\) nhé :))
Ta có: \(B=\frac{9}{9\cdot19}+\frac{9}{19\cdot29}+\frac{9}{29\cdot39}+...+\frac{9}{2009\cdot2019}\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{10}{9\cdot19}+\frac{10}{19\cdot29}+\frac{10}{29\cdot39}+...+\frac{10}{2009\cdot2019}\right)\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{1}{9}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{2009}-\frac{1}{2019}\right)\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{1}{9}-\frac{1}{2019}\right)=\left(\frac{9}{10}\cdot\frac{1}{9}\right)-\left(\frac{9}{10}\cdot\frac{1}{2019}\right)\)
\(\Rightarrow B=\frac{1}{10}-\frac{9}{20190}=\frac{2019}{20190}-\frac{9}{20190}=\frac{2010}{20190}=\frac{201}{2019}=\frac{67}{673}\)
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