ta có:

1-1/2+1/2-1/3+1/3-1/4+....+1/x -1/x+1 =499/500

1-1/x+1 =499/500

1/x+1 =1/500 

x+1=500

x=499

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{X\times\left(X+1\right)}=\frac{499}{500}\)

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{X}-\frac{1}{X+1}=\frac{499}{500}\)

\(\Leftrightarrow1-\frac{1}{X+1}=\frac{499}{500}\)

\(\Leftrightarrow\frac{1}{X+1}=\frac{1}{500}\)

\(\Leftrightarrow X+1=500\)

\(\Leftrightarrow X=499\)

a) -287 + 499 + (-499) + 285

=-287+285

=-2

b: Ta có: \(1992+\left(-53\right)+158+\left(-247\right)+\left(-1592\right)\)

\(=\left(1992-1592\right)+\left(-53-247\right)+158\)

\(=400-300+158=258\)

\(\frac{1}{3}+\frac{1}{6}=\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{499}{1000}\)

\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=\frac{499}{1000}\)

\(\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x\left(x+1\right)}=\frac{499}{1000}\)

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{499}{1000}\)

\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{499}{1000}\)

\(2\left(\frac{1}{2}-\frac{1}{x-1}\right)=\frac{499}{1000}\)

\(\frac{1}{2}-\frac{1}{x-1}=\frac{499}{2000}\)

\(\frac{2000\left(x-1\right)}{2\left(x-1\right)2000}-\frac{2.2000}{\left(x-1\right)2.2000}=\frac{499.2\left(x-1\right)}{2000.2\left(x-1\right)}\)

Khử mẫu 

\(2000x-2000-4000=998x-998\)

\(2000x-6000=998x-998\)

\(1002x-5002=0\)

\(1002x=5002\Leftrightarrow x=\frac{2501}{501}\)

theo bai co 1/3+1/6+...+2/x.x+1=499/1000

(=)2/2.3+2/3.4+...+2/x.(x+1)=499/1000

(=)2(1/2-...-1/x+1)=499/1000

(=)1/2-1/x+1=499/2000

(=)1/x+1=501/2000

den day thi minh chiu roi!

\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{x+1}=\frac{499}{500}\)

1 - 499/500 = 1/x + 1

1/500 = 1/x+1

x + 1 = 500

x = 499

a) 1/1.2 + 1/2.3 + 1/3.4 + .... + 1/x.(x+1) = 499/500

1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/x - 1/x+1 = 499/500

1 - 1/x+1 = 499/500

1/x+1 = 1 - 499/500

1/x+1 = 1/500

x + 1 = 500

     x = 500 - 1 

     x = 499

b) 1/1.3 + 1/3.5 + 1/5.7 + .... + 1/x.(x+2) = 20/41

1/2 . [ 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/x.(x+2) ] = 20/41

1/2 . [ 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/x - 1/x+2 ] = 20/41

1/2 . [ 1 - 1/x+2 ) = 20/41

1 - 1/x+2 = 20/41 : 1/2

1 - 1/x+2 = 40/41

1/x+2 = 1 - 40/41

1/x+2 = 1/41

x + 2 = 41

      x = 41 - 2 

      x = 39

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow x=499\)

giúp e vs

a: 3^x=243

=>3^x=3^5

=>x=5

b: 4^x=4096

=>4^x=4^5

=>x=5

c: 5^3-x=25

=>3-x=2

=>x=1

d: =>2x-3=3

=>2x=6

=>x=3

j: =>2^x*8+2^x*2=80

=>2^x=8

=>x=3