\(A=\dfrac{202\cdot209+10}{202\cdot211-394}\)

\(A=\dfrac{202\cdot209+10}{202\cdot209+2\cdot202-394}\)

\(A=\dfrac{202\cdot209+10}{202\cdot209+10}\\ A=1\)

\(\dfrac{6}{3\cdot5}+\dfrac{6}{5\cdot7}+\dfrac{6}{7\cdot9}+.....+\dfrac{6}{33\cdot35}\)

\(=\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{33\cdot35}\right)\cdot3\)

\(=\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+.....+\dfrac{1}{33}-\dfrac{1}{35}\right)\cdot3\)

\(=\left(\dfrac{1}{3}-\dfrac{1}{35}\right)\cdot3\)

\(=\dfrac{32}{3\cdot35}\cdot3\)

\(=\dfrac{32}{35}\)

\(\left(9x+2\right)\cdot3=60\\ 9x+2=20\\ 9x=18\\ x=2\)

\(1,6x+\dfrac{2}{5}=-0,448\\ 1,6x=-0,448-0,4\\ 1,6x=-0,848\\ -x=0,53\)

=> chọn C

\(\left(\dfrac{9}{10}+\dfrac{1}{10}:\dfrac{4}{5}\right)\times\left(\dfrac{4}{5}-\dfrac{2}{5}\times\dfrac{4}{3}\times\dfrac{9}{8}\right)\)

\(=\left(\dfrac{9}{10}+\dfrac{1}{8}\right)\times\left(\dfrac{4}{5}-\dfrac{3}{5}\right)\)

\(=\left(\dfrac{36}{40}+\dfrac{5}{40}\right)\times\dfrac{1}{5}\)

\(=\dfrac{41}{40}\times\dfrac{1}{5}\)

\(=\dfrac{41}{200}\)

1.

A=n.n+n

A=n(n+1)

+) Nếu n là số tự nhiên chẵn thì => n+1 là số tự nhiên lẻ

Vì chẵn x lẻ  = chẵn => A ⋮ 2 nếu n là chắn

+) Nếu n là số tự nhiên lẻ thì => n+1 là số tự nhiên chẵn

Vì lẻ x chẵn = chẵn  => A ⋮ 2 nếu n là lẻ

Đã CMR: A  ⋮ 2 

2. 

\(I=99-97+95-93+91-89+....+7-5+3-1\\ I=\left(99+95+91+...+7+3\right)-\left(97+93+.....+5+1\right)\\ I=\left[\left(99-3\right):4+1\right]\cdot\left(99+3\right):2-\left[\left(97-1\right):4+1\right]\cdot\left(97+1\right):2\\ I=25\cdot102:2-25\cdot98:2\\ I=1275-1225\\ I=50\)

\(\dfrac{54\times50+49\times100}{37\times38+126\times19}\)

\(=\dfrac{50\times\left(49\times2+54\right)}{38\times\left(63+37\right)}\)

\(=\dfrac{50\times152}{38\times100}\)

\(=\dfrac{25\times2\times4\times38}{38\times25\times4}\)

\(=2\)

Ta có: \(\left(x+16\right)⋮\left(x+1\right)\)

=> x + (1+15) ⋮ ( x+1)

=> (x+1) + 15  ⋮ ( x+1)

Vì  ( x+1) ⋮ ( x+1) => 15  ⋮ ( x+1)

=>  ( x+1) ϵ Ư(15)

Ư(15) = {-1;1;-3;3;-15;15;5;-5}

=>x = {-2;0;-4;2;-16;14;4;-6}

1 can đựng số lít nước là:

25 : 5 = 5(lít nước)

9 can đụng số lít nước là: 

5 x 9 = 45 ( lít nước)

Đ/s:.....

Gọi số cần tìm là:\(\overline{abc}\)

ta biết:

\(\overline{7abc7}-\overline{abc}=71861\\ 70007+\overline{abc}\cdot10-\overline{abc}=71861\\ \overline{abc}\cdot9=1854\\ \overline{abc}=206\)