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Bài 2:
\(A=2+2^2+2^3+...+2^{60}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)
\(A=2\cdot\left(1+2\right)+2^3\cdot\left(1+2\right)+...+2^{59}\cdot\left(1+2\right)\)
\(A=2\cdot3+2^3\cdot3+...+2^{59}\cdot3\)
\(A=3\cdot\left(2+2^3+...+2^{59}\right)\) ⋮ 3
Vậy: A ⋮ 3
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\(A=2+2^2+...+2^{60}\)
\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)
\(A=2\cdot\left(1+2+4\right)+2^4\cdot\left(1+2+4\right)+...+2^{58}\cdot\left(1+2+4\right)\)
\(A=2\cdot7+2^4\cdot7+...+2^{58}\cdot7\)
\(A=7\cdot\left(2+2^4+....+2^{58}\right)\) ⋮ 7
Vậy: A ⋮ 7
___________________
\(A=2+2^2+...+2^{60}\)
\(A=\left(2+2^3\right)+\left(2^2+2^4\right)+...+\left(2^{58}+2^{60}\right)\)
\(A=2\cdot\left(1+4\right)+2^2\cdot\left(1+4\right)+...+2^{58}\cdot\left(1+4\right)\)
\(A=2\cdot5+2^2\cdot5+...+2^{58}\cdot5\)
\(A=5\cdot\left(2+2^2+...+2^{58}\right)\) ⋮ 5
Vậy: A ⋮ 5
\(\Rightarrow\)x+2\(\in\)Ư(9)
Ư(9)={\(\pm1\); \(\pm3\); \(\pm9\)}
\(\Rightarrow\)x+2\(\in\left\{\pm1;\pm3;\pm9\right\}\)
\(\Rightarrow\)x\(\in\left\{\pm1;-3;-5;-11;7\right\}\)
Vậy x\(\in\left\{\pm1;-3;-5;-11;7\right\}\)
4: =4+5+{12+(-8)-(-8)-(-5)+(-12)+16-5+3}
=9+[12+5-12+16-5+3}
=9+19=28
5: =15-[13+8-10-16]-{5-7+9-3}
=15-(-5)-4
=15+5-4
=20-4
=16
m) 63.83-9.7.(-17)
= 5229-63.(-17)
= 5229 - (-1071)
= 5229 + 1071
= 6300
n) 42.3 - 7[(-34)+18]
= 126 - 7. (-16)
= 126 - (-112)
=126+112
= 238
\(p,71\cdot70+35\cdot\left(-7\right)-13\cdot35\)
\(=4970+\left(-245\right)-455=4725-455=4270\)
\(q,18\cdot\left(23-17\right)-13\cdot\left(23+18\right)\)
\(=18\cdot6-13\cdot41=108-533=-425\)
g: =(32-34)+(36-38)+(40-42)
=(-2)+(-2)+(-2)
=-6
l: =-5-{-[7-10]-[5+12]}-[-3+9-4-5]
=-5+(-3)+17-[-3]
=-8+17+3
=20-8=12
9: =>x-2/3=1/5*-7/15=-7/75
=>x=-7/75+50/75=43/75
11: =>x-4/5=3/10*(-7)/3=-7/10
=>x=-7/10+4/5=8/10-7/10=1/10
12:=>7/5*9+x=4/9
=>x=4/9-63/5=-547/45
10: =>x+5/6=-8/147
=>x=-87/98
\(1,-\dfrac{5}{12}\left(\dfrac{4}{9}+-\dfrac{5}{16}\right)\\ =-\dfrac{5}{12}\left(\dfrac{64}{144}+-\dfrac{45}{144}\right)\\ =-\dfrac{5}{12}.\dfrac{19}{144}\\ =-\dfrac{95}{1728}\\ 2,\left(-0,75+\dfrac{1}{2}\right)\left(\dfrac{1}{3}-\dfrac{1}{4}\right)\\ =\left(-\dfrac{3}{4}+\dfrac{1}{2}\right)\left(\dfrac{4}{12}-\dfrac{3}{12}\right)\\ =\left(-\dfrac{3}{4}+\dfrac{2}{4}\right).\dfrac{1}{12}\\ =-\dfrac{1}{4}.\dfrac{1}{12}\\ =-\dfrac{1}{48}\\ 3,-\dfrac{5}{7}.\dfrac{4}{13}+-\dfrac{5}{7}.\dfrac{9}{13}+-\dfrac{5}{7}\\ =-\dfrac{5}{7}.\dfrac{4}{13}+-\dfrac{5}{7}.\dfrac{9}{13}+-\dfrac{5}{7}.1=-\dfrac{5}{7}\left(\dfrac{4}{13}+\dfrac{9}{13}+1\right)\\ =-\dfrac{5}{7}\left(\dfrac{4}{13}+\dfrac{9}{13}+\dfrac{13}{13}\right)\\ =-\dfrac{5}{7}.\dfrac{26}{13}\\ =-\dfrac{5}{7}.2\\ =-\dfrac{10}{7}\)
=205 mà đề là tính hả
80 - (-5)3
= 80+ 53
= 80+ 125
=205