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Lời giải:
$A=1+(3+3^2+3^3)+(3^4+3^5+3^6)+....+(3^{2014}+3^{2015}+3^{2016})$
$=1+3(1+3+3^2)+3^4(1+3+3^2)+...+3^{2014}(1+3+3^2)$
$=1+3.13+3^4.13+....+3^{2014}.13$
$=1+13(3+3^4+...+3^{2014})$
$\Rightarrow A-1\vdots 13(1)$
Mặt khác:
$A=1+(3+3^2+3^3+3^4)+....+(3^{2013}+3^{2014}+3^{2015}+3^{2016})$
$=1+3(1+3+3^2+3^3)+....+3^{2013}(1+3+3^2+3^3)$
$=1+(3+...+3^{2013})(1+3+3^2+3^3)$
$=1+40(3+....+3^{2013})$
$\Rightarrow A-1\vdots 5(2)$
Từ $(1); (2)$ mà $(5,13)=1$ nên $A-1\vdots (5.13)$ hay $A-1\vdots 65$
$\Rightarrow A$ chia $65$ dư $1$
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ta có: \(\frac{31+32+35}{34}=\frac{31}{34}+\frac{32}{34}+\frac{35}{34}.\)
mà \(\frac{31}{32}>\frac{31}{34};\frac{32}{33}>\frac{32}{34}\)
\(\Rightarrow\frac{31}{32}+\frac{32}{33}+\frac{35}{34}>\frac{31}{34}+\frac{32}{34}+\frac{35}{34}=\frac{31+32+35}{34}\)
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a)5^3 . 37+5^3 . 64 - 5^7 : 5^4
=5^3 . (37+64) - 5^3
=125 . 101- 125
=12625-125
=12500
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+) \(176+483+24+117\)
\(=\left(176+24\right)+\left(483+117\right)\)
\(=200+600\)
\(=800\)
+) \(239+518+761+482\)
\(=\left(239+761\right)+\left(518+482\right)\)
\(=1000+1000\)
\(=2000\)
+) \(32+33+34+...+78+79+80\)
Số số hạng của dãy là :
\(\left(80-32\right):1+1=49\) (số)
Tổng của dãy là :
\(\frac{\left(80+32\right)\times49}{2}=2744\)
+) \(5\times125\times2\times4\)
\(=\left(5\times2\right)\times\left(125\times4\right)\)
\(=10\times500\)
\(=5000\)
+) \(25\times50\times4\times20\)
\(=\left(25\times4\right)\times\left(50\times20\right)\)
\(=100\times1000\)
\(=100000\)
+) \(17\times32+43\times17+17\times25\)
\(=17\times\left(32+43+25\right)\)
\(=17\times100\)
\(=1700\)
+) \(24\times19+29\times24+18\times24+24\times33+24\)
\(=24\times\left(19+29+18+33+1\right)\)
\(=24\times100\)
\(=2400\)
_Chúc bạn học tốt_
![](https://rs.olm.vn/images/avt/0.png?1311)
a) (-x+31)-39=-69
-x+31=-69+39
-x+31=-30
-x=-30-31
-x=-61
=> x=61
b) -120-(-30-x)=-50
-30-x=-120-(-50)
-30-x=-70
x=-30-(-70)
x=40
c) 17+x- [ 352-(-400)]=-32
17+x-752=-32
17+x=-32+752
17+x=720
x=720-17
x=703
đúng nha
3E=32-33+34-35+...+32016-32017
3E-E=32-32017
2E=9-32017
E=9-32017/2
T..i..c..k nha
3E=3.(3-32+33-...-32016)
3E+E=(32-33+...-32015+32016)+(3-32+33-...-32016)
4E=(-32+32)+(-33+33)+...+(-32015+32015)+(32016+3)
4E=32016+3
E=32016+3 : 3