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6: =>x=9/10+1/5=9/10+2/10=11/10
7: =>x=3/8-5/12=36/96-40/96=-1/24
8: =>x=7/6-5/4=14/12-15/12=-1/12
9: =>x=1/35+2/7=1/35+10/35=11/35
10: =>x=2/7-7/10=20/70-49/70=-29/70
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1: =>x=-5/3-1/2=-13/6
2: =>x=1/3-3/5=-4/15
4: =>x=-7/9+4/3=-7/9+12/9=5/9
5: =>x=5/6-7/3=5/6-14/6=-9/6=-3/2
6: =>x=9/10+1/5=11/10
7: =>x=3/8-5/12=36/96-40/96=-1/24
8: Đề sai rồi bạn
![](https://rs.olm.vn/images/avt/0.png?1311)
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 $36S=1-\frac{69.7-7-69}{7^{70}}=1-\frac{407}{7^{70}}$
$\Rightarrow S=\frac{1}{36}(1-\frac{407}{7^{70}})$
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
$A=\frac{1}{7^2}+\frac{2}{7^3}+\frac{3}{7^4}+....+\frac{69}{7^{70}}$
$7A=\frac{1}{7}+\frac{2}{7^2}+\frac{3}{7^3}+...+\frac{69}{7^{69}}$
$\Rightarrow 6A=7A-A=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{69}}-\frac{69}{7^{70}}$
$42A=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}}$
$\Rightarrow 36A=42A-6A=1-\frac{69}{7^{69}}+\frac{69}{7^{70}}<1$
$\Rightarrow A< \frac{1}{36}$
![](https://rs.olm.vn/images/avt/0.png?1311)
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Bằng 5^57/7,71 cách giải 12:0,1+7/^1-729=5^57/7,71
5^57/7,71-3:3x2+2:4=5^57/7,71
Chúc bạn học giỏi nhe :)))) 👍👍👍👍👍👍👍👍👍
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a) \(\dfrac{5}{24}+x=\dfrac{7}{12}\)
<=> \(x=\dfrac{7}{12}-\dfrac{5}{24}=\dfrac{14}{24}-\dfrac{5}{24}=\dfrac{9}{24}=\dfrac{3}{8}\)
b) \(x-\dfrac{3}{4}=\dfrac{1}{2}\)
<=> \(x=\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{5}{4}\)
c) bn ghi rõ đề chút
A = \(\dfrac{1}{7}\) + \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\) +.......+\(\dfrac{1}{7^{68}}\)+\(\dfrac{1}{7^{69}}\)
7. A = 1 + \(\dfrac{1}{7}\) + \(\dfrac{1}{7^2}\) + \(\dfrac{1}{7^3}\)+......+ \(\dfrac{1}{7^{68}}\)
7A - A = 1 - \(\dfrac{1}{7^{69}}\)
A = ( 1 - \(\dfrac{1}{7^{69}}\)):6