a, \(\frac{5}{11.16}+\frac{5}{11.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

=\(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

=\(\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

a, A=1/11-1/16+1/16-1/21+1/21-1/26+...+1/61-1/66

      = 1/11-1/66=5/66 ( A chính là biểu thức ở phần a)

b, 1/12+1/20+1/30+...+1/110

=1/3.4+1/4.5+1/5.6+..+1/10.11

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11

=1/3-1/11=8/33

b,\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\) 

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

=\(\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)

a)  \(x^2+y^2=\left(x+y\right)^2-2xy=1^2-2.\left(-6\right)=13\)

    \(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=1^3-3.\left(-6\right).1=19\)

\(x^5+y^5=\left(x^2+y^2\right)\left(x^3+y^3\right)-x^2y^2\left(x+y\right)=13.19-\left(-6\right)^2.1=211\)

b)  \(x^2+y^2=\left(x-y\right)^2+2xy=1^1+2.6=13\)

    \(x^3-y^3=\left(x-y\right)^3+3xy\left(x-y\right)=1^3+3.6.1=19\)

   \(x^5-y^5=\left(x^2+y^2\right)\left(x^3-y^3\right)+x^2y^2\left(x-y\right)=13.19+6^2.1=283\)

Đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\Rightarrow x=2k,y=3k,z=5k\)

Ta có: xyz = 810 => 2k.3k.5k = 810 => 30k³ = 810 => k³ = 27 => k = 3

=> x = 6, y = 9, z = 15

810 nha

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=210

1+2+3+4+5+6+7=28

a)dãy trên có 20 số hạng , vậy tổng là:

(20 + 1) x 20 : 2 = 210

b) làm tương tự bài a

(20-1)+1=20 số hạng

vậy tính tổng ta làm như sau:

(20+1).20:2(chia 2 bởi vì có 2 cặp)=210

vậy tổng trên là 210

Tìm x . biết : 

\(a,\frac{2}{5}:\left(-x-\frac{1}{2}\right)=\frac{4}{5}\)

\(\Rightarrow-x-\frac{1}{2}=\frac{2}{5}:\frac{4}{5}\)

\(\Rightarrow-x-\frac{1}{2}=\frac{2}{5}.\frac{5}{4}\)

\(\Rightarrow-x-\frac{1}{2}=\frac{1}{2}\)

\(\Rightarrow-x=\frac{1}{2}+\frac{1}{2}\)

\(\Rightarrow-x=1\)

\(\Rightarrow x=-1\)

Vậy \(x=-1\)

a. \(\frac{2}{5}.\left(-x-\frac{1}{2}\right)=\frac{4}{5}\)

\(\Rightarrow-x-\frac{1}{2}=\frac{2}{5}:\frac{4}{5}\)

\(\Rightarrow-x-\frac{1}{2}=\frac{2}{5}.\frac{5}{4}\)

\(\Rightarrow-x-\frac{1}{2}=\frac{1}{2}\)

\(\Rightarrow-x=\frac{1}{2}+\frac{1}{2}\)

\(\Rightarrow-x=1\)

\(\Rightarrow x=-1\)

A , 34 - \(\dfrac{x}{30}\) = \(\dfrac{5}{6}\) 

             \(\dfrac{x}{30}\) = 34 - \(\dfrac{5}{6}\)

             \(\dfrac{x}{30}=\) \(\dfrac{199}{6}\)

               \(\dfrac{x}{30}=\) \(\dfrac{995}{30}\)

                x = 995

B x +\(\dfrac{13}{34}\) = \(\dfrac{12}{17}\)

   x          = \(\dfrac{12}{17}-\dfrac{13}{34}\)  

   x         = \(\dfrac{11}{34}\) 

\(\dfrac{7}{9}=\dfrac{21}{27};\dfrac{7}{10}=\dfrac{21}{30}\) 

hai số nằm giữa \(\dfrac{7}{9}\) và \(\dfrac{7}{10}\) 

\(\dfrac{21}{27}>\dfrac{21}{28}>\dfrac{21}{29}>\dfrac{21}{30}\) 

\(\dfrac{13}{15}=\dfrac{91}{105};\dfrac{14}{15}=\dfrac{98}{105}\)

6 số nằm giữa \(\dfrac{13}{15}\) và \(\dfrac{14}{15}\) 

\(\dfrac{91}{105}< \dfrac{92}{105};\dfrac{93}{105};\dfrac{94}{105};\dfrac{95}{105};\dfrac{96}{105};\dfrac{97}{105}< \dfrac{98}{105}\)

mk cần gáp ó

Gọi (12n+1, 24n+1) = d   \(\left(d\inℕ^∗\right)\)

\(\Rightarrow\)12n+1\(⋮\)d và 24n+1\(⋮\)d

\(\Rightarrow\)(12n+1) - (24n+1)\(⋮\)d

\(\Rightarrow\)(24n+2) - (24n+1)\(⋮\)d

\(\Rightarrow\)1\(⋮\)d

\(\Rightarrow\)d=1

Do đó, (12n+1, 24n+1) = 1

Vậy (12n+1, 24n+1) = 1 với n\(\in\)N*.

a) 3/4 + -1/8 = 5/8

b)-5/12 + -7/24 = -9/8

c) 4/21 - -5/28 = 31/84

d) 1 + -7/28 = 3/4

e) -4/3 - 17/6= -25/6

f) 1/3 - ( 1/2 +1/8 )= -7/24

g)1/21 - ( 1/7 - 1/3 ) = 5/21

h)1/2 - 1/4 + 1/13 + 1/8= 47/104

a) x - 1/10 = 1/15

x=1/15+1/10

b) -4/21 - x = -3/7

c) x + 1/2 = 3/4 - (-1/2)

x+1/2= 5/4

x= 5/4-1/2

x=3/4

Vay x=3/4

d) 4/7 - x = 1/3 - (-2/3)