2x-1/2-1/16-1/12-....-1/49.50=7-1/50+x
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-...-\dfrac{1}{49\cdot50}=7-\dfrac{1}{50}+x\)
\(\Leftrightarrow2x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=x+\dfrac{349}{50}\)
\(\Leftrightarrow2x-\dfrac{49}{50}-x-\dfrac{349}{50}=0\)
=>x=398/50=199/25
![](https://rs.olm.vn/images/avt/0.png?1311)
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 = \(\frac{199}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-....-\frac{1}{49.50}=7+\frac{1}{50}+x\)
\(2x-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{49.50}\right)=7+\frac{1}{50}+x\)
\(2x-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{49.50}\right)=7+\frac{1}{50}+x\)
\(2x-\left(\frac{1}{1}-\frac{1}{50}\right)=7+\frac{1}{50}+x\)
\(2x-1+\frac{1}{50}=7+\frac{1}{50}+x\)
=> 2x - 1 = 7 + x
=> 2x - x = 7 + 1
=> x = 8
![](https://rs.olm.vn/images/avt/0.png?1311)
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 = \(\dfrac{174}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\right)\) =\(\frac{349}{50}+x\)
\(x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\) \(=\frac{349}{50}\)
\(x-\left(1-\frac{1}{50}\right)=\frac{349}{50}\)
\(x-\frac{49}{50}=\frac{349}{50}\)
\(x=\frac{199}{25}\)
=> 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
\(2x-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-....-\dfrac{1}{49.50}=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{49.50}\right)=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=7-\dfrac{1}{50}+x\)\(\Rightarrow2x-1+\dfrac{1}{50}=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x=7-\dfrac{1}{50}+x-\dfrac{1}{50}+1\)
\(\Rightarrow2x=\dfrac{199}{25}+x\)
\(\Rightarrow x=\dfrac{199}{25}\)