a: \(\frac{52}{17}>\frac{51}{17}=3\)

\(3=\frac{121}{41}>\frac{120}{41}\)

Do đó: \(\frac{52}{17}>\frac{120}{41}\)

b: \(\frac34+\frac14:\left(\frac{7}{12}-\frac16\right)\)

\(=\frac34+\frac14:\left(\frac{7}{12}-\frac{2}{12}\right)\)

\(=\frac34+\frac14:\frac{5}{12}\)

\(=\frac34+\frac14\times\frac{12}{5}=\frac34+\frac35=\frac{15}{20}+\frac{12}{20}=\frac{27}{20}\)

c: \(372,463\cdot998+744,926\)

\(=372,463\cdot998+372,463\cdot2\)

\(=372,463\times\left(998+2\right)=372,463\times1000=372463\)

d: Số số hạng trong dãy số 2;4;6;...;100 là:

\(\left(100-2\right):2+1=98:2+1=49+1=50\) (số)

\(2-4+6-8+10-12+\cdots+98-100+102\)

\(=\left(2-4\right)+\left(6-8\right)+\cdots+\left(98-100\right)+102\)

=(-2)+(-2)+...+(-2)+102

\(=-2\cdot\frac{50}{2}+102=-50+102=52\)

e: (y+112)-113=79

=>y+112-113=79

=>y-1=79

=>y=79+1=80

f: \(\frac34-y=\frac12\)

=>\(y=\frac34-\frac12=\frac14\)

g: \(\left(\frac45-2\times y\right)+\frac16=\frac56\)

=>\(\frac45-2\times y=\frac56-\frac16=\frac46=\frac23\)

=>\(2\times y=\frac45-\frac23=\frac{12}{15}-\frac{10}{15}=\frac{2}{15}\)

=>\(y=\frac{2}{15}:2=\frac{1}{15}\)

h: (y+1)+(y+2)+...+(y+50)=1750

=>50y+(1+2+...+50)=1750

=>\(50y+50\times\frac{51}{2}=1750\)

=>50y+1275=1750

=>50y=1750-1275=475

=>\(y=\frac{475}{50}=9,5\)

Đặt :

\(A=\)\(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}\)

\(A=\dfrac{1}{5}+\left(\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}\right)+\left(\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}\right)\)

Ta thấy :

\(\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}< \dfrac{1}{12}+\dfrac{1}{12}+\dfrac{1}{12}\)

\(\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}< \dfrac{1}{60}+\dfrac{1}{61}+\dfrac{1}{62}\)

\(\Rightarrow A< \dfrac{1}{5}+\left(\dfrac{1}{12}+\dfrac{1}{12}+\dfrac{1}{12}\right)+\left(\dfrac{1}{60}+\dfrac{1}{60}+\dfrac{1}{60}\right)\)

\(\Rightarrow A< \dfrac{1}{5}+\dfrac{1}{12}.3+\dfrac{1}{60}.3\)

\(\Rightarrow A< \dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}\)

\(\Rightarrow A< \dfrac{10}{20}=\dfrac{1}{2}\)

\(\Rightarrow A< \dfrac{1}{2}\rightarrowđpcm\)

( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . (  65 . 111 - 13 . 15 . 37)

=( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . (  13. 5 . 3. 37 - 13 . 15 

37)

=( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . (  13. 15 . 37 - 13 . 15 

37)

=( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . 0

=0

\(\left(1+2+...+100\right)\cdot\left(1^2+2^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\)

\(=\left[65\cdot111\left(1-1\right)\right]\cdot\left(1+2+...+100\right)\cdot\left(1^2+2^2+...+10^2\right)\)

=0

( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . (  65 . 111 - 13 . 15 . 37)

=( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . (  13. 5 . 3. 37 - 13 . 15 

37)

=( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . (  13. 15 . 37 - 13 . 15 

37)

=( 1 + 2 + .... + 99 + 100 ) . ( 1² + 2² + .... + 10²) . 0

=0

j mà  nhìu zu zậy làm bao giờ mới xong

Ủng hộ mk đi các bạn
 

khó quá mk giải miết mà không ra

khó vãi