Tìm z,y,z thuộc Z, biết: 1/3.4 + 1/4.5 + 1/5.6 + ... + 2/ x(x+1) = 3/10
Tìm \(x\in Z\), biết:
\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x\left(x+1\right)}=\frac{3}{10}\)
1/3.4+1/4.5+1/5.6+.....+1/x(x+1)=3/10
1/3-1/4+1/4-1/5+1/5-........-1/x+1/x-1/x+1=3/10
=>1/3-1/x+1=3/10
1/x+1=3/10-1/3=1/30
=>x+1=30
x=30-1
x=29
Ta có :
\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x\left(x+1\right)}=\frac{3}{10}\)
=>\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{3}{10}\)
=>\(\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)
=>\(\frac{1}{x+1}=\frac{1}{3}-\frac{3}{10}\)
=>\(\frac{1}{x+1}=\frac{1}{30}\)
=>\(x+1=30\)
=>\(x=30-1\)
=>\(x=29\)
Vậy \(x=29\)
1) 3x-5y/2=7y-3z/3=5z-7x/4 và x+y+z=17
Tìm x,y,z
2) CM: 1/1.2+1/3.4+1/5.6+.............+1/49.50=1/26+1/27+1/28+.........+1/50
\(2\)
CMR
\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+....+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\left(\frac{1}{1}+\frac{1}{3}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{50}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{25}\)
\(=\frac{1}{26}+\frac{1}{27}+....+\frac{1}{50}\left(đpcm\right)\)
tìm x, biết
1/3.4+1/4.5+1/5.6+1/6.7+...+1/x.(x+1)=3/10
(1/3-1/4+1/4-1/5+1/5-.......+1/x.(x+1)=3/10
1/3-1/x+1=3/10
tự làm...
tìm x biết:
1/3.4+1/4.5+1/5.6+1/6.7+....+1/x(x+1)=3/10
1/3.4+1/4.5+1/5.6+1/6.7+....+1/x(x+1)=3/10
<=> \(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{\left(x+1\right)x}=\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)
<=> \(\frac{1}{x+1}=\frac{1}{3}-\frac{3}{10}=\frac{1}{30}\)=> x+1=30=>x=29
\(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{x\left(x+1\right)}=\frac{3}{10}\)
\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{3}{10}\)
\(\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)
\(\frac{1}{x+1}=\frac{1}{3}-\frac{3}{10}\)
\(\frac{1}{x+1}=\frac{1}{30}\)
\(\Rightarrow x+1=30\)
\(x=30-1=29\)
Tìm \(x\in Z\), biết:
\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x\left(x+1\right)}=\frac{3}{10}\)
Quá dễ:
=> 1/3 - 1/4 + 1/4 - 1/5 + ....+ 1/x - 1/x+1 = 3/10
=> 1/3 - 1/x+1 = 3/10
=> 1/x+1 = 1/3 - 3/10
Còn lại tự làm nhá!
<=> 1/3 - 1/(x+1) = 3/10
<=> 1/(x+1) = 1/30
=> x+1 = 30
<=> x= 29
= > 1/3 - 1/4 +1/4 -1/5 + ..... + 1/x - 1/x+1 = 3/10
= > 1/3 - 1/x+1 = 3/10
= > 1/x+1 = 1/3 - 3/10
= > 1/x+1 =1/30
= > x+1 = 30
= > x = 29
Vậy x = 29
tìm n thuộc N biết:
\(\dfrac{1}{3.4}\)+\(\dfrac{1}{4.5}\)+\(\dfrac{1}{5.6}\)+....+\(\dfrac{1}{n\left(n+1\right)}\)=\(\dfrac{3}{10}\)
\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{n.\left(n+1\right)}=\dfrac{3}{10}\)
\(\Rightarrow\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{3}{10}\)
\(\Rightarrow\dfrac{1}{3}-\dfrac{1}{n+1}=\dfrac{3}{10}\)
\(\Rightarrow\dfrac{1}{n+1}=\dfrac{1}{30}\)
\(\Rightarrow n+1=30\)
\(\Rightarrow n=29\)
Vậy n = 29.
Tìm n thuộc N :
1/3.4 + 1/4.5 + 1/5.6 + .... + 1/n( n+1 ) = 3/10
\(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + .....+\(\dfrac{1}{n.(n+1)}\) = \(\dfrac{3}{10}\)
\(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\) +......+ \(\dfrac{1}{n}-\dfrac{1}{n+1}\) = \(\dfrac{3}{10}\)
\(\dfrac{1}{3}-\dfrac{1}{n+1}\) = \(\dfrac{3}{10}\)
\(\dfrac{1}{n+1}\) = \(\dfrac{1}{3}-\dfrac{3}{10}\)
\(\dfrac{1}{n+1}\) = \(\dfrac{1}{30}\)
n + 1 = 30
n = 30 - 1
n = 29
Kết luận n = 29 là giá trị thỏa mãn yêu cầu đề bài.
Tìm n thuộc n :
1/3.4 + 1/4.5 + 1/5.6 + ... + 1/n( n+1 ) = 3/10
\(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}+...+\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{3}{10}\)
\(\dfrac{1}{3}-\dfrac{1}{n+1}=\dfrac{3}{10}\)
\(\dfrac{-1}{\left(n+1\right)}=\dfrac{-1}{30}\)
\(-n-1=-30\)
-n = -29
n = 29
Tìm x:
1/3.4+1/4.5+1/5.6+1/6.7+....+1/x(x+1)=3/10