\(P=10^n-18n-1\)

\(=\left(10^n-1\right)-9.2n\)

\(=99...9-9.2n\)

 ( 9 chữ số 9 ) 

Vì \(\hept{\begin{cases}99...9\left(nso9\right)⋮9\\9.2n⋮9\end{cases}}\)

\(\Rightarrow\left(99...9-9.2n\right)⋮9\)

 ( n chữ số 9 )

Hay \(P⋮9\left(đpcm\right)\)

Sửa cho anh chút dòng 3 là 

99...9

( n sô 9 ) nha

\(\text{a)}\left(2^{17}+17^2\right)\left(9^{15}-15^9\right)\left(4^2-2^4\right)\)

\(=\left(2^{17}+17^2\right)\left(9^{15}-15^9\right)\left[\left(2^2\right)^2-2^4\right]\)

\(=\left(2^{17}+17^2\right)\left(9^{15}-15^9\right)\left(2^4-2^4\right)\)

\(=\left(2^{17}-17^2\right)\left(9^{15}-15^9\right).0\)

\(=0\)

\(\text{b)}\left(7^{1997}-7^{1995}\right):\left(7^{1994}.7\right)=\frac{7^{1997}-7^{1995}}{7^{1994}.7}=\frac{7^{1995}\left(7^2-1\right)}{7^{1995}}=7^2-1=48\)

\(A=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(=\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

\(\frac{1}{100}-\left(1-\frac{1}{100}\right)=\frac{1}{100}+\frac{1}{100}-1=\frac{1}{50}-1=-\frac{49}{50}\)

C = 1/100 - 1/100.99 - 1/99.98 - 1/98.97 -...- 1/3.2 - 1/2.1

C = 1/100 - ( 1/1.2 + 1/2.3 + ...+ 1/98.99 + 1/99.100 )

C = 1/100 - ( 1+1/2 + 1/2 - 1/3 + ...+ 1/98 - 1/99 + 1/99 - 1/100 )

C = 1/100 - ( 1 - 1/100 )

C = 1/100 - 99/100

C = - 98/100

C = - 49/50

Đổi \(3\frac{1}{2}=\frac{7}{2}\)

Quả dưa cân nặng số kg là :

          \(\frac{7}{2}:\frac{3}{4}=\frac{14}{3}\)(kg)

                         Đáp số : \(\frac{14}{3}kg\)

\(3\frac{1}{2}=\frac{7}{2}kg\) 

Quả dưa nặng:

\(\frac{7}{2}.\frac{3}{4}=\frac{21}{8}kg\)

Vậy:...

\(a,\left|x+5\right|-7< 20\)

\(\Rightarrow\left|x+5\right|< 20+7\)

\(\Rightarrow\left|x+5\right|< 27\)

\(\Rightarrow\hept{\begin{cases}x+5< 27\\x+5>-27\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x< 27-5\\x>-27-5\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x< 22\\x>-32\end{cases}}\)

\(\Rightarrow x\in\left\{-31;-30;...;20;21\right\}\)

\(b,\left|x+18\right|+13>21\)

\(\Rightarrow\left|x+18\right|>21-13\)

\(\Rightarrow\left|x+18\right|>8\)

\(\Rightarrow\orbr{\begin{cases}x+18>8\\x+18< -8\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x>-10\\x< -26\end{cases}}\)

\(\Rightarrow x\in\left\{...;-28;-27;-9;-8;...\right\}\)

~Study well~

#KSJ

diện tích làm vườn là:

   150:100*60=90 (m2)

diện tích xây nhà là:

      150-90=60(m2)

          đ/s:60 m2

diện tích xây nhà là:

\(150-\left(150.\frac{60}{100}\right)=60\left(m^2\right)\)

đáp số:60 m2

2n + 7 = 2.(n-2) + 11 chia hết cho n-2 => 11 chia hết cho n-2

Ukm...đề bảo tìm n hả bạn???

\(2n+7⋮n-2\)

\(\Leftrightarrow2\left(n-2\right)+11⋮n-2\)

Vì : \(2\left(n-2\right)⋮n-2\forall n\)nên \(11⋮n-2\)

\(\Leftrightarrow n-2\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)

\(\Leftrightarrow n\in\left\{3;1;-9;13\right\}\)

Vậy : \(n\in\left\{3;1;-9;13\right\}\)

Chắc vậy!!! Rất vui vì giúp đc bạn !!!