1/1*2 + 1/2*3 +1/3*4 +.....+ 1/x(x+1) =499/500
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24 tháng 11 2019
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
24 tháng 11 2019
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{X\times\left(X+1\right)}=\frac{499}{500}\)
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{X}-\frac{1}{X+1}=\frac{499}{500}\)
\(\Leftrightarrow1-\frac{1}{X+1}=\frac{499}{500}\)
\(\Leftrightarrow\frac{1}{X+1}=\frac{1}{500}\)
\(\Leftrightarrow X+1=500\)
\(\Leftrightarrow X=499\)
12 tháng 8 2021
b: Ta có: \(1992+\left(-53\right)+158+\left(-247\right)+\left(-1592\right)\)
\(=\left(1992-1592\right)+\left(-53-247\right)+158\)
\(=400-300+158=258\)
TD
1
12 tháng 6 2020
\(\frac{1}{3}+\frac{1}{6}=\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{499}{1000}\)
\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=\frac{499}{1000}\)
\(\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x\left(x+1\right)}=\frac{499}{1000}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{499}{1000}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{499}{1000}\)
\(2\left(\frac{1}{2}-\frac{1}{x-1}\right)=\frac{499}{1000}\)
\(\frac{1}{2}-\frac{1}{x-1}=\frac{499}{2000}\)
\(\frac{2000\left(x-1\right)}{2\left(x-1\right)2000}-\frac{2.2000}{\left(x-1\right)2.2000}=\frac{499.2\left(x-1\right)}{2000.2\left(x-1\right)}\)
Khử mẫu
\(2000x-2000-4000=998x-998\)
\(2000x-6000=998x-998\)
\(1002x-5002=0\)
\(1002x=5002\Leftrightarrow x=\frac{2501}{501}\)
NH
1
26 tháng 5 2016
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!
10 tháng 1 2016
\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{x+1}=\frac{499}{500}\)
1 - 499/500 = 1/x + 1
1/500 = 1/x+1
x + 1 = 500
x = 499
18 tháng 8 2015
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
HP
3 tháng 9 2021
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{499}{500}\)
\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{499}{500}\)
\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{499}{500}\)
\(\Leftrightarrow x=499\)
HL
1
24 tháng 7 2023
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