tính S =1/2.5+1/5.8+1/8.11+1/11.14+...+1/2021.2024
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NV
1
CX
12 tháng 5 2016
S = 1/2.5 +1/5.8 +1/8.11+1/11.14+1/14.17+1/17.20
S=1/3.(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)
S=1/3.(1/2-1/20)
S=1/3.(10/20-1/20)
S=1/3.9/20
S= 3/20
k nha
TV
3
12 tháng 5 2015
Ta có : \(\frac{3x}{2\times5}+\frac{3x}{5\times8}+\frac{3x}{8\times11}+\frac{3x}{11\times14}=\frac{1}{21}\)
\(\Rightarrow x\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}\right)=\frac{1}{21}\)
\(\Rightarrow x\times\left(\frac{1}{2\times5}+\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}\right)=\frac{1}{21}\)
\(x\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\right)=\frac{1}{21}\)
\(x\times\left(\frac{1}{2}-\frac{1}{14}\right)\) \(=\frac{1}{21}\)
\(x\times\frac{3}{7}\) \(=\frac{1}{21}\)
\(x\) \(=\frac{1}{21}\div\frac{3}{7}=\frac{1}{21}\times\frac{7}{3}\)
\(\Rightarrow x=\frac{1}{9}\)
6 tháng 5 2018
Ta có 3x/2.5+3x/5.8+3x/8.11+3x/11.14=1/21
=>x(3/2.5+3/5.8+3/8.11+3/11.14)=1/21
=>3x(1/2.5+1/5.8+1/8.11+1/11.14)=1/21
=>3x(1/2-1/14)=1/21
=>3x.3/7=1/21
=>3x=1/21:3/7
=>3x=1
=>x=1:3=1/3
28 tháng 3 2017
\(\frac{1}{3}.\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right]\)
\(\frac{1}{3}\left[\frac{1}{2}-\frac{1}{20}\right]=\frac{1}{3}.\frac{9}{20}=\frac{3}{20}\)
mk đầu tiên đó
MB
4
12 tháng 5 2015
3x/2.5 + 3x/5.8+3x/8.11+3x/11.14 = 1/21
x(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14) = 1/21
x(1/2-1/14) = 1/21
x . 3/7 = 1/21
=> x = 1/21 : 3/7
=> x = 1/9
Hihi mình giải zầy mk hk bik đúng hay sai
BV
3
6 tháng 6 2021
`(3x)/(2.5)+(3x)/(5.8)+(3x)/(8.11)+(3x)/(11.14)=1/21`
`=>x(3(2.5)+3/(5.8)+3/(8.11)+3/(11.14))=1/21`
`=>x(1/2-1/5+1/5-1/8+1/8-1/11-1/14)=1/21`
`=>x*(1/2-1/14)=1/21`
`=>x*3/7=1/21`
`=>x=1/21:3/7=1/9`
Vậy `x=1/9`
TK
1
VT
4 tháng 4 2022
\(x\) \((\)\(\dfrac{3}{2.5}\) \(+
\) \(\dfrac{3}{5.8}\) \(+\) \(\dfrac{3}{8.11}\) \(+\) \(\dfrac{3}{11.14}\)\()\) \(=\) \(\dfrac{1}{21}\)
\(x\) \((\)\(\dfrac{1}{2}\) \(-\) \(\dfrac{1}{5}\) \(+\) \(\dfrac{1}{5}\) \(-\) \(\dfrac{1}{8}\) \(+\) \(\dfrac{1}{8}\) \(-\) \(\dfrac{1}{11}\) \(+\) \(\dfrac{1}{11}\) \(-\) \(\dfrac{1}{14}\)\()\) \(=\) \(\dfrac{1}{21}\)
\(x\) \((\)\(\dfrac{1}{2}\) \(-\) \(\dfrac{1}{14}\)\()\) \(=\) \(\dfrac{1}{21}\)
\(x\) x \(\dfrac{3}{7}\) \(=\) \(\dfrac{1}{21}\)
\(x\) \(=\) \(\dfrac{1}{21}\) \(:\) \(\dfrac{3}{7}\)
\(x\) \(=\) \(\dfrac{1}{9}\)
1 tháng 4 2023
\(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}+\dfrac{3}{14\cdot17}\)
= \(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}\)
\(=\dfrac{1}{2}-\dfrac{1}{17}\)
\(=\dfrac{15}{34}\)
Vì \(\dfrac{15}{34}< \dfrac{1}{2}=>\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}+\dfrac{3}{14\cdot27}< \dfrac{1}{2}\)
NT
1
TM
12 tháng 5 2017
A=...
<=>\(A=\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{1}{17.20}\right)\)
<=>\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)
<=>\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)\)
<=>\(A=\frac{1}{6}-\frac{1}{60}< \frac{1}{6}< 1\)
\(S=\dfrac{1}{2\cdot5}+\dfrac{1}{5\cdot8}+...+\dfrac{1}{2021\cdot2024}\)
\(=\dfrac{1}{3}\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+...+\dfrac{3}{2021\cdot2024}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{2021}-\dfrac{1}{2024}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{2024}\right)=\dfrac{1}{3}\cdot\dfrac{1011}{2024}=\dfrac{337}{2024}\)
3S=3/2.5+3/5.8+3/8.11+3/11.14+...+3/2021.2024
3S=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+...+1/2021-1/2024
3S=1/2-1/2024
3S=1011/2024
S=1011/2024:3
S=337/2024