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26 tháng 5 2022
\(2x-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-...-\dfrac{1}{49\cdot50}=7-\dfrac{1}{50}+x\)
\(\Leftrightarrow2x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=x+\dfrac{349}{50}\)
\(\Leftrightarrow2x-\dfrac{49}{50}-x-\dfrac{349}{50}=0\)
=>x=398/50=199/25
NL
1
HT
14 tháng 7 2015
2x - \(\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-....-\frac{1}{49.50}\)= 7-\(\frac{1}{50}\)+x
2x - x - \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{49.50}\right)\)= 7 - \(\frac{1}{50}\)
x - \(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\)= \(\frac{349}{50}\)
x - \(\left(1-\frac{1}{50}\right)\)=\(\frac{349}{50}\)
x - \(\frac{49}{50}\)=\(\frac{349}{50}\)
x = \(\frac{349}{50}+\frac{49}{50}\)
x = \(\frac{199}{25}\)
4 tháng 9 2017
2x - \(\dfrac{1}{2}-\dfrac{1}{6}-...-\dfrac{1}{49.50}\)= 6-\(\dfrac{1}{50}\) + x
<=> x - ( \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\)) = \(\dfrac{299}{50}\)
<=> x - \(\left(1-\dfrac{1}{50}\right)\) = \(\dfrac{299}{50}\)
<=> x - \(\dfrac{49}{50}\) = \(\dfrac{299}{50}\)
<=> x = \(\dfrac{174}{25}\)
4 tháng 9 2017
\(2x-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-....-\dfrac{1}{49.50}=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{49.50}\right)=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=7-\dfrac{1}{50}+x\)\(\Rightarrow2x-1+\dfrac{1}{50}=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x=7-\dfrac{1}{50}+x-\dfrac{1}{50}+1\)
\(\Rightarrow2x=\dfrac{199}{25}+x\)
\(\Rightarrow x=\dfrac{199}{25}\)
18 tháng 6 2017
\(2x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-....-\frac{1}{49.50}=7+\frac{1}{50}+x\)
\(2x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{49.50}\right)=7+\frac{1}{50}+x\)
\(2x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{49.50}\right)=7+\frac{1}{50}+x\)
\(2x-\left(\frac{1}{1}-\frac{1}{50}\right)=7+\frac{1}{50}+x\)
\(2x-1+\frac{1}{50}=7+\frac{1}{50}+x\)
=> 2x - 1 = 7 + x
=> 2x - x = 7 + 1
=> x = 8
6 tháng 8 2017
\(2x-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\right)\) =\(\frac{349}{50}+x\)
\(x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\) \(=\frac{349}{50}\)
\(x-\left(1-\frac{1}{50}\right)=\frac{349}{50}\)
\(x-\frac{49}{50}=\frac{349}{50}\)
\(x=\frac{199}{25}\)
6 tháng 8 2017
=> 2x- ( 1/2+1/6+1/12+..._1/ 49.50 )= 7-1/50+x
=> 2x -( 1/1.2 + 1/2.3+1/3.4+...+1/49.50)= 7-1/50+x
=> 2x - ( 1- 1/2+ 1/2-1/3+1/3-1/4+...+1/49-1/50) = 7-1/50 + x
=> 2x - ( 1-1/50) =7-1/50 + x
=> 2x- 1+ 1/50=7-1/50+ x
=> 1+1/50= 2x- (7 - 1/50+ x)
=> 1+1/50 = 2x- 7 + 1/50- x
=> 1+1/50 = x + 1/50 - 7
=> 1 = x + 1/50 - 7 - 1/50
=> 1 = x - 7
=> x = 7+ 1
=> x = 8
I
6 tháng 6 2021
1
Ta có :A=1/1.2+1/3.4+...+1/99.100=1/2+1/12+...+1/9900
7/12=1/2+1/12
Vì 1/2+1/12<1/2+1/12+...+1/9900
Nên: 7/12<A (1)
Lại có:A=1/1.2+1/3.4+...+1/99.100
=1-1/2+1/3-1/4+...+1/99-1/100
=(1-1/2+1/3)+(-1/4+1/5-1/6)+...+(-1/98+1/99-1/100)
5/6=1-1/2+1/3
vì: 1-1/2+1/3 < (1-1/2+1/3)+(-1/4+1/5-1/6)+...+(-1/98+1/99-1/100)
nên 5/6 < A (2)
Từ (1) và (2) suy ra 7/12<A<5/6
DL
24 tháng 8 2019
1/1.2+1/3.4+1/5.6+...+1/49.50
=1/1-1/2+1/3-1/4+...+1/49-1/50
=1/1+1/2+1/3+1/4+...+1/49+1/50-2(1/2+1/4+1/6+...+1/50)
=1/1+1/2+1/3+1/4+...+1/49+1/50-(1/1+1/2+1/3+1/4+...+1/25)
=1/26+1/27+...+1/50=1/26+1/27+...+1/50(đpcm)
b. 1/1-1/2+1/3-1/4+...+1/99-1/100=99/100
7/12=175/300; 5/6=10/12=250/300; 99/100=297/300
(hình như khúc này đề bài sai hả bạn) bạn tự tính ra nhé
bài 2: a.x+1/10+x/12+x/14+...x+1/20
(x+x+x...+x)+(1/10+1/12+...+1/20)
ko có kết quả sao tìm x được bạn:[
b.x+1/2000+x+2/1999=x+3/1998+x+4/1997
x+1/2000+x+2/1999=x+3/1998+x+4/1997
(x+1/2000+1)+(x+2/1999+1)=(x+3/1998+1)+(x+4/1997+1)
x+2002/2000+x+2002/1999=x+2002/1998+x+2002/1997
x+2002(1/2000+1/1999)=(x+2002)(1/1998+1/1997)
=>(1/2000+1/1999)=(1/1998+1/1997)
x+2002(1/2000+1/1999)-(x+2002)(1/1998+1/1997)=0
(x+2002)(1/2000+1/1999-1/1998-1/1997)=0
(x+2002).0=0
(x+2002)=0
x =0-2002=-2002
Chúc bạn học tốt.
3 tháng 9 2016
a)A = 1 / (1*2) + 1 / (3*4) + ... + 1 / (99*100) > 1 / (1*2) + 1 / (3*4) = 1 / 2 + 1 / 12 = 7 / 12 ♦
A = 1 / (1*2) + 1 / (3*4) + ... + 1 / (99*100) = (1 - 1 / 2) + (1 / 3 - 1 / 4) + ... + (1 / 99 - 100) =
(1 - 1 / 2 + 1 / 3) - (1 / 4 - 1 / 5) - (1 / 6 - 1 / 7) - ... - (1 / 98 - 1 / 99) - 1 / 100 <
1 - 1 / 2 + 1 / 3 = 5 / 6 ♥
♦, ♥ => 7 / 12 < A < 5 / 6
b)ta có:
1/1.2+1/3.4+1/5.6+...+1/49.50
=>1-1/2+1/3-1/4+1/5-1/6+...+1/49-1/50
=>(1+1/3+1/5+1/7+...+1/49)-(1/2+1/4+1/6+...+1/50)
=>(1+1/2+1/3+...+1/49+1/50)-(1/2+1/4+1/6+...+1/50).2
=>(1+1/2+1/3+...+1/49+1/50) -( 1+1/2+1/3+...+1/25)
=>1/26+1/27+1/28+...+1/50=1/26+1/27+1/28+...+1/50
hay 1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+1/28+...+1/50