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\(\dfrac{-1}{12},\dfrac{-3}{4},\dfrac{2}{9},\dfrac{7}{6}\)
`1/5 . 4/7 + 3/7 . 1/5 -1/5`
`=1/5 . 4/7 + 3/7 . 1/5 -1/5 . 1`
`=1/5 . ( 4/7+3/7-1)`
`=1/5 . ( 7/7-1)`
`= 1/5 . 0`
`=0`
\(\dfrac{1}{5}\times\dfrac{4}{7}+\dfrac{3}{7}\times\dfrac{1}{5}-\dfrac{1}{5}=\dfrac{1}{5}\times\left(\dfrac{4}{7}+\dfrac{3}{7}-1\right)=\dfrac{1}{5}\times0=0\)
MSC : `24`
`-5/6=-5.4/6.4=-20/24`
`7/8=7.3/8.3=21/24`
`7/24=7/24`
`-3/4=-3.6/4.6=-18/24`
`2/3=2.8/3.8=16/24`
`1=24/24`
Sắp xếp các phân số sau theo thứ tự tăng dần :
`-20/24;-18/24;7/24;16/24;21/24;24/24`
\(\dfrac{-1}{9}.\dfrac{-3}{5}+\dfrac{5}{-6}.\dfrac{-3}{5}-\dfrac{7}{2}.\dfrac{3}{5}\)
\(=\dfrac{3}{5}.\left(\dfrac{1}{9}+\dfrac{5}{6}-\dfrac{7}{2}\right)\)
\(=\dfrac{3}{5}.\left(\dfrac{2}{18}+\dfrac{15}{18}-\dfrac{63}{18}\right)\)
\(=\dfrac{3}{5}.\left(-\dfrac{23}{9}\right)\)
\(=-\dfrac{69}{45}\)
\(-\dfrac{5}{7}\times\dfrac{2}{13}+\dfrac{-5}{7}\times\dfrac{3}{13}-\dfrac{5}{7}\times\dfrac{8}{13}\)
\(=-\dfrac{5}{7}\left(\dfrac{2}{13}+\dfrac{3}{13}+\dfrac{8}{13}\right)\)
\(=-\dfrac{5}{7}\times\dfrac{13}{13}\)
\(=-\dfrac{5}{7}\times1=-\dfrac{5}{7}\)
Lời giải:
$S=\frac{1}{7^2}+\frac{2}{7^3}+\frac{3}{7^4}+...+\frac{69}{7^{70}}$
$7S=\frac{1}{7}+\frac{2}{7^2}+\frac{3}{7^3}+...+\frac{69}{7^{69}}$
$6S=7S-S=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{69}}-\frac{69}{7^{70}}$
$42S=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}}$
$\Rightarrow 42S-6S=(1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}})-(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{69}}-\frac{69}{7^{70}})$
$\Rightarrow 36S=1-\frac{69}{7^{69}}-\frac{1}{7^{69}}+\frac{69}{7^{70}}$
Hay $36S=1-\frac{69.7-7-69}{7^{70}}=1-\frac{407}{7^{70}}$
$\Rightarrow S=\frac{1}{36}(1-\frac{407}{7^{70}})$
`5/9+4/9:x=1/3`
`=>4/9:x=1/3-5/9`
`=>4/9:x=3/9-5/9`
`=>4/9:x=-2/9`
`=>x=4/9:(-2/9)`
`=>x=4/9.(-9/2)`
`=>x=-4/2`
`=>x=-2`
3A=3/1X4 + 3/4X7 + ...+3/298X301
3A=1/1-1/4+1/4-1/7+...+1/298-1/301
3A=1/1+(-1/4+1/4)+(-1/7+1/7)+...+(-1/298+1/298)-1/301
3A=1/1+0+0+0+0+0+...+0-1/301
3A=1/1-1/301
3A=301/301-1/301
3A=300/301
A=300/301:3
A=300/301X1/3
A=300/903
A=100/301
QUA CHI TIET
TICK VOI
A= 1/3 + 1/3^2 + ... + 1/3^8
3A= 3. (1/3+ 1/3^2+ ... + 1/3^8)
3A=1+ 1/3 + 1/3^2+ ... +1/3^7
=> 3A - A= (1 + 1/3 + 1/3^2 + ... + 1/3^7) - (1/3 + 1/3^2+ ... + 1/3^8)
=> 2A= 1 - 1/ 3^8
2A= 6560/6561
A= 6560/6561 : 2
A= 3280/6561
\(C=\dfrac{-5}{7}+\dfrac{-2}{7}+\dfrac{3}{4}+\dfrac{1}{4}+\dfrac{-1}{5}=-1+1-\dfrac{1}{5}=\dfrac{-1}{5}\)