tính A=11/3+11/5+11/35+...+11/99
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11 tháng 8 2016
\(\left(\frac{99^9}{11^9}-\frac{99^{99}}{11^{99}}-\frac{99^{999}}{11^{999}}\right)\left(\frac{1}{5}-\frac{1}{7}-\frac{2}{35}\right)\)
\(=\left(\frac{99^9}{11^9}-\frac{99^{99}}{11^{99}}-\frac{99^{999}}{11^{999}}\right)\left(\frac{7}{35}-\frac{5}{35}-\frac{2}{35}\right)\)
\(=\left(\frac{99^9}{11^9}-\frac{99^{99}}{11^{99}}-\frac{99^{999}}{11^{999}}\right).0\)
\(=0\)
PG
2
17 tháng 3 2023
`4/15+35/99+11/15-2/7+64/99-5/7`
`=(4/15+11/15)+(35/99+64/99)-(2/7+5/7)`
`=15/15+99/99-7/7`
`=1+1-1`
`=2-1`
`=1`
PG
1
22 tháng 5 2022
Bài 1:
\(=\dfrac{-1}{2}+\dfrac{3}{5}-\dfrac{1}{9}+\dfrac{1}{131}+\dfrac{2}{7}+\dfrac{4}{35}-\dfrac{7}{18}\)
\(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{131}\)
\(=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}+\dfrac{1}{131}\)
=1/131
Bài 2:
b: \(B=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)
\(=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{99}-\dfrac{98}{99}=-\dfrac{97}{99}\)
B
1
31 tháng 7 2015
A = 5/3.7 + 5/7.11 + 5/11.15 + ... + 5/35.39
A = 5/4 x ( 4/3.7 + 4/7.11 + 4/11.15 + ... + 4/35.39 )
A = 5/4 x ( 1/3 - 1/7 + 1/7 - 1/11 + 1/11 - 1/15 + ... + 1/35 - 1/39 )
A = 5/4 x ( 1/3 - 1/39 )
A = 5/4 x 4/13
A = 5/13
ND
1
31 tháng 7 2015
\(A=\frac{5}{3\cdot7}+\frac{5}{7\cdot11}+\frac{5}{11\cdot15}+...+\frac{5}{35\cdot39}\)
\(=\frac{5}{4}\cdot\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+...+\frac{4}{35\cdot39}\right)\)
\(=\frac{5}{4}\cdot\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...-\frac{1}{35}+\frac{1}{35}-\frac{1}{39}\right)\)
\(=\frac{5}{4}\cdot\left(1-\frac{1}{39}\right)=\frac{5}{4}\cdot\frac{38}{39}=\frac{95}{78}\)
8 tháng 4 2018
1 Tính
7/12 - 2/7 + 1/12= (7/12-1/12)+2/7=6/12+2/7=1/2+2/7=7/14+4/14=11/14
12/17-5/17-4/17= 12-5-4/17=3/17
2a, 7/11+3/4+4/11+1/4= (7/11+4/11)+3/4+1/4=11/11+4/4=1+1=2
b)72/99-28/99-14/99= (72-28-14)/99=30/99=10/33
c)69,78+35,97+30,22= (69,78+30,22)+35,97=100+35,97=135,97
d) 83,45-30,98-42,47=83,45-(30,98+42,47)=83,45-73,45=10
TP
0
NM
1
S
14 tháng 5 2023
\(\dfrac{x}{3}+\dfrac{x}{15}+\dfrac{x}{35}+...+\dfrac{x}{99}=2023\times\dfrac{5}{11}\)
\(\dfrac{x}{1.3}+\dfrac{x}{3.5}+\dfrac{x}{5.7}+...+\dfrac{x}{9.11}=2023\times\dfrac{5}{11}\)
\(x-\dfrac{x}{3}+\dfrac{x}{3}-\dfrac{x}{5}+\dfrac{x}{5}-\dfrac{x}{7}+...+\dfrac{x}{9}-\dfrac{x}{11}=2023\times\dfrac{5}{11}\)
\(x-\dfrac{x}{11}=2023\times\dfrac{5}{11}\)
\(\dfrac{11\times x-x}{11}=2023\times\dfrac{5}{11}\)
\(\dfrac{10\times x}{11}=2023\times\dfrac{5}{11}\)
\(\dfrac{10}{11}\times x=2023\times\dfrac{5}{11}\)
\(x=2023\times\dfrac{5}{11}:\dfrac{10}{11}\)
\(x=\dfrac{2023}{2}=1011,5\)
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