Đặt A=\(\dfrac{1}{11}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{13}\)+...\(\dfrac{1}{69}\)+\(\dfrac{1}{70}\)

         =(\(\dfrac{1}{11}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{13}\)+...\(\dfrac{1}{19}\)+\(\dfrac{1}{20}\))+(\(\dfrac{1}{21}\)+\(\dfrac{1}{22}\)+\(\dfrac{1}{23}\)+...+\(\dfrac{1}{29}\)+\(\dfrac{1}{30}\))+(\(\dfrac{1}{31}\)+\(\dfrac{1}{32}\)+\(\dfrac{1}{33}\)+...+\(\dfrac{1}{59}\)+\(\dfrac{1}{60}\))+...+\(\dfrac{1}{70}\)

Nhận xét:

\(\dfrac{1}{11}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{13}\)+...+\(\dfrac{1}{19}\)+\(\dfrac{1}{20}\)>\(\dfrac{1}{20}\)+\(\dfrac{1}{20}\)+...+\(\dfrac{1}{20}\)=\(\dfrac{10}{20}\)=\(\dfrac{1}{2}\)

\(\dfrac{1}{21}\)+\(\dfrac{1}{22}\)+\(\dfrac{1}{23}\)+...+\(\dfrac{1}{29}\)+\(\dfrac{1}{30}\)>\(\dfrac{1}{30}\)+\(\dfrac{1}{30}\)+...+\(\dfrac{1}{30}\)=\(\dfrac{10}{30}\)=\(\dfrac{1}{3}\)

\(\dfrac{1}{31}\)+\(\dfrac{1}{32}\)+\(\dfrac{1}{33}\)+...+\(\dfrac{1}{59}\)+\(\dfrac{1}{60}\)>\(\dfrac{1}{60}\)+\(\dfrac{1}{60}\)+...+\(\dfrac{1}{60}\)=\(\dfrac{30}{60}\)=\(\dfrac{1}{2}\)

=>A>\(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)+\(\dfrac{1}{2}\)+\(\dfrac{1}{61}\)+...+\(\dfrac{1}{69}\)+\(\dfrac{1}{70}\)>\(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)+\(\dfrac{1}{2}\)=\(\dfrac{4}{3}\)

=>A>\(\dfrac{4}{3}\)

Vậy: \(\dfrac{1}{11}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{13}\)+...+\(\dfrac{1}{69}\)+\(\dfrac{1}{70}\)>\(\dfrac{4}{3}\) (ĐPCM)

Thấy đúng cho 1 tick và 1 follow nha!

Chúc bạn học tốt!

số học sinh xếp loại văn hóa giỏi là

     50:10x3=15(h/sinh)

số học sinh còn lại là

    50-15=35(h/sinh)

số học sinh loại khá là

    35:8x3=

Bài 4:

a: (x+1)(y-2)=3

=>(x+1;y-2)∈{(1;3);(3;1);(-1;-3);(-3;-1)}

=>(x;y)∈{(0;5);(2;3);(-2;-1);(-4;1)}

b: (2x-1)(3y+1)=12

mà 2x-1 lẻ

nên (2x-1;3y+1)∈{(1;12);(-1;-12);(3;4);(-3;-4)}

=>(2x;3y)∈{(2;11);(0;-13);(4;3);(-2;-5)}

mà 3y⋮3

nên (2x;3y)∈{(4;3)}

=>(x;y)∈{(2;1)}

c: xy-x+y-2=0

=>x(y-1)+y-1-1=0

=>(x+1)(y-1)=1

=>(x+1;y-1)∈{(1;1);(-1;-1)}

=>(x;y)∈{(0;2);(-2;0)}

Bài 3:

a: 3n-1⋮n+2

=>3n+6-7⋮n+2

=>-7⋮n+2

=>n+2∈{1;-1;7;-7}

=>n∈{-1;-3;5;-9}

b:2n+3⋮3n-1

=>6n+9⋮3n-1

=>6n-2+11⋮3n-1

=>11⋮3n-1

=>3n-1∈{1;-1;11;-11}

=>3n∈{2;0;12;-10}

=>n∈{2/3;0;4;-10/3}

mà n là số nguyên

nên n∈{0;4}

đề thi hả bn

ko, chỉ là btvn thôi nhé, mình nhầm

a: (326-43)+(174-57)

=326-43+174-57

=500-100

=400

b: (351-875)-(125-149)

=351-875-125+149

=500-1000

=-500

c: \(-415-\left\lbrace-215-\left\lbrack-115-\left(-315-2016\right)\right\rbrack\right\rbrace\)

=-415+215+[-115+315+2016]

=-200+[200+2016]

=-200+200+2016

=2016

d: [461+(-78)+40]+(-461)

=461-78+40-461

=-78+40

=-38

e: -323+[(-874)+564-241]
=-323-241+564-874

=-564+564-874

=-874

f: [(-59)+71]-[-83-(-95)]

=-59+71-(-83+95)

=12-12

=0

theo cong thuc tinh so duong thang di qua cac cap diem voi n diem (trong do khong co 3 diem nao thang hang )ta co 

n.(n-1):2=78

n.(n-1)=78.2

n.(n-1)=156

n.(n-1)=12.13

=>n=13

vay so diem can tim la 13 diem 

c: =547x100=54700

d: =-76x10=-760

b: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{-1;-3;3;-7\right\}\)

d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

Bài 4:

a) Áp dụng t/c dtsbn:

\(\dfrac{x}{4}=\dfrac{y}{3}=\dfrac{x+y}{4+3}=\dfrac{14}{7}=2\Rightarrow\left\{{}\begin{matrix}x=2.4=8\\y=2.3=6\end{matrix}\right.\)

Vậy....

b) Áp dụng t/c dtsbn:

\(\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{2x}{16}=\dfrac{3y}{36}=\dfrac{2x+3y}{16+36}=\dfrac{13}{52}=\dfrac{1}{4}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{4}.8=2\\y=\dfrac{1}{4}.12=3\end{matrix}\right.\)(nhận)

Vậy...