Chịu

Khó quá, mình không biết giải.

(75% x \(\frac12\)) : |-1\(\frac23\)| - \(\frac{5}{27}\) x 1,8 x 2018\(^0\)

= (\(\frac34\) x \(\frac12\)) : |\(-\frac53\)|- \(\frac{5}{27}\) x \(\frac95\) x 1

= \(\frac38\) : \(\frac53\) - \(\frac13\)

= \(\frac38\times\frac35\) - \(\frac13\)

= \(\frac{9}{40}\) - \(\frac13\)

= \(\frac{27}{120}-\frac{40}{120}\)

= \(-\frac{13}{120}\)

-9.7+4.(-2)=-63+-8=-71

( -9 ) . | - 5 + 2 | + 4 . ( 7 - 9 )

= (-9)*3+4*(-2)

=-35 

a: \(D=\frac{1}{1\cdot1981}+\frac{1}{2\cdot1982}+\cdots+\frac{1}{25\cdot2005}\)

\(=\frac{1}{1980}\left(\frac{1980}{1\cdot1981}+\frac{1980}{2\cdot1982}+\cdots+\frac{1980}{25\cdot2005}\right)\)

\(=\frac{1}{1980}\left(1-\frac{1}{1981}+\frac12-\frac{1}{1982}+\cdots+\frac{1}{25}-\frac{1}{2005}\right)\)

\(=\frac{1}{1980}\left(1+\frac12+\cdots+\frac{1}{25}-\frac{1}{1981}-\frac{1}{1982}-\cdots-\frac{1}{2005}\right)\)

\(E=\frac{1}{1\cdot26}+\frac{1}{2\cdot27}+\cdots+\frac{1}{1980\cdot2005}\)

\(=\frac{1}{25}\left(\frac{25}{1\cdot26}+\frac{25}{2\cdot27}+\cdots+\frac{25}{1980\cdot2005}\right)\)

\(=\frac{1}{25}\left(1-\frac{1}{26}+\frac12-\frac{1}{27}+\cdots+\frac{1}{1980}-\frac{1}{2005}\right)\)

\(=\frac{1}{25}\left(1+\frac12+\cdots+\frac{1}{25}-\frac{1}{1981}-\frac{1}{1982}-\cdots-\frac{1}{2005}\right)\)

DO đó: \(\frac{D}{E}=\frac{1}{1980}:\frac{1}{25}=\frac{25}{1980}=\frac{5}{396}\)

b: \(A=133\left(\frac{1}{1\cdot1996}+\frac{1}{2\cdot1997}+\cdots+\frac{1}{17\cdot2012}\right)\)

\(=\frac{133}{1995}\left(\frac{1995}{1\cdot1996}+\frac{1995}{2\cdot1997}+\cdots+\frac{1995}{17\cdot2012}\right)\)

\(=\frac{1}{15}\left(1-\frac{1}{1996}+\frac12-\frac{1}{1997}+\cdots+\frac{1}{17}-\frac{1}{2012}\right)\)

\(=\frac{1}{15}\left(1+\frac12+\cdots+\frac{1}{17}-\frac{1}{1996}-\frac{1}{1997}-\cdots-\frac{1}{2012}\right)\)

\(B=\frac{17}{15}\left(\frac{1}{1\cdot18}+\frac{1}{2\cdot19}+\cdots+\frac{1}{1995\cdot2012}\right)\)

\(=\frac{1}{15}\left(\frac{17}{1\cdot18}+\frac{17}{2\cdot19}+\cdots+\frac{17}{1995\cdot2012}\right)\)

\(=\frac{1}{15}\left(1-\frac{1}{18}+\frac12-\frac{1}{19}+\cdots+\frac{1}{1995}-\frac{1}{2012}\right)\)

\(=\frac{1}{15}\left(1+\frac12+\cdots+\frac{1}{17}-\frac{1}{1996}-\frac{1}{1997}-\cdots-\frac{1}{2012}\right)\)

Do đó: A=B

Gọi số nguyên tố nhỏ nhất là \(a\), 2 số tiếp theo cách nhau 4 đơn vị là:
\(a + 4\) và \(a + 8\)

Ta thử với \(a = 3\), được 3 số là: 3, 7, 11
→ Cả 3 số đều là số nguyên tố

Vậy ba số nguyên tố cần tìm là:

\(\boxed{3;7;11}\)

3,7,11

(4n+3) chia hết cho 2n+1 <=> 2n+1 thuộc Ư(4n+3)= {4n+3 , -4n-3}

 giải tìm n