(3n−1)⋮n−1

=>(3n−1)−3⋅(n−1)⋮n−1

$\left(3n-1\right)-3\cdot \left(n-1\right)$

$=3n-1-3n+3$

$=\left(3n-3n\right)+\left(-1+3\right)$

$=0+2=2$

$\backslash (=>2⋮n-1\backslash )$

$\backslash (=>\backslash left(n-1\backslash right)\backslash inƯ\backslash left(2\backslash right)\backslash )$

Ư(2) = {-1;1;-2;2}

Th1

n-1=-1

=> n=0

Th2

n-1=1

=> n=2

Th3

n-1=-2

=> n=-1

Th4

n-1=2

=> n= 3

Vậy n ϵ {3;-1;2;0}

Mình làm lại lúc nãy mình hơi lag

\(\left(3n-1\right)⋮n-1\\ =>\left(3n-1\right)-3\cdot\left(n-1\right)⋮n-1\)

\(\left(3n-1\right)-3\cdot\left(n-1\right)\\ =3n-1-3n+3\\ =\left(3n-3n\right)+\left(-1+3\right)\\ =0+2\\ =2\)

\(=>2⋮n\\ =>n\inƯ\left(2\right)\\ Ư\left(2\right)=\left\{1;-2;2;-1\right\}\)

\(Th1:3n-1=1\\ 3n=2\\ n=\dfrac{2}{3}\)

\(Th2:3n-1=-2\\ 3n=-1\\ =n=-\dfrac{1}{3}\)

\(Th3:3n-1=2\\ 3n=3\\ n=1\)

\(Th4:3n-1=-1\\ 3n=0\\ n=0\)

\(=>n\in\left\{0;1;-\dfrac{1}{3};\dfrac{2}{3}\right\}\)

= (2014 - 2012) : 25

= 2 : 25

= 0,08

S hình thang là

3,6 * 1,5 : 2= 2,7 (m²)

Đ/s: 2,7m²

\(\dfrac{x}{8}=\dfrac{9}{13}\)

\(x\cdot\dfrac{1}{8}=\dfrac{9}{13}\)

\(x=\dfrac{9}{13}\cdot8\)

\(x=\dfrac{72}{13}\)

\(B=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+....+\dfrac{1}{8^2}< 1\)

\(\dfrac{1}{2^2}< \dfrac{1}{2}\)

\(\dfrac{1}{3^2}< \dfrac{1}{2\cdot3}\)

.......

\(\dfrac{1}{8^2}< \dfrac{1}{7\cdot8}\)

\(=>B=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+....+\dfrac{1}{8^2}< \dfrac{1}{2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+.....+\dfrac{1}{7\cdot8}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}+.....+\dfrac{1}{7}-\dfrac{1}{8}=1-\dfrac{1}{8}< 1\)

\(=>B< 1\)

C

\(\dfrac{1}{5}+Y=7\\ Y=7-\dfrac{1}{5}\\ Y=\dfrac{35}{5}-\dfrac{1}{5}\\ Y=\dfrac{34}{5}\)

\(Y\div\dfrac{3}{4}=\dfrac{5}{7}\\ Y=\dfrac{5}{7}\times\dfrac{3}{4}\\ Y=\dfrac{15}{28}\)

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+....+\dfrac{1}{19\cdot20}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{20}\)

\(A=1-\dfrac{1}{20}\)

\(A=\dfrac{19}{20}\)

\(B=2+4+6+...+98+100-99-97-...-3-1\\ B=2+4+6+...+98+100+\left(-99\right)+\left(-97\right)+...+\left(-3\right)+\left(-1\right)\\ B=\left[2+\left(-1\right)\right]+\left[4+\left(-3\right)\right]+....\left[100+\left(-99\right)\right]\\ B=1+1+...+1\\ B=50\cdot1\\ B=50\)