tìm x :x+3\4.7+3\4.7+3\10.13+...+3\37+40=-37/40.GIẢI HỘ MÌNH
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VN
Võ Ngọc Phương
VIP
21 tháng 8 2023
\(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+\dfrac{1}{10.13}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{34}{103}\)
\(\dfrac{1}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)=\dfrac{34}{103}\)
\(\dfrac{1}{3}.\left(1-\dfrac{1}{x+3}\right)=\dfrac{34}{103}\)
\(1-\dfrac{1}{x+3}=\dfrac{34}{103}:\dfrac{1}{3}=\dfrac{34}{103}.3\)
\(1-\dfrac{1}{x+3}=\dfrac{102}{103}\)
\(\dfrac{1}{x+3}=1-\dfrac{102}{103}=\dfrac{103}{103}-\dfrac{102}{103}\)
\(\dfrac{1}{x+3}=\dfrac{1}{103}\)
\(\Rightarrow x+3=103\)
\(x=103-3\)
\(x=100\)
Vậy x = 100
12 tháng 5 2016
\(=3.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\right)=3.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(=3.\left(1-\frac{1}{100}\right)=\frac{297}{100}\)
HT
3
10 tháng 5 2022
\(=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{2021}-\dfrac{1}{2024}=\dfrac{1}{4}-\dfrac{1}{2024}=\dfrac{505}{2024}\)
10 tháng 5 2022
\(\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{1}{2021.2024}\)
=\(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{14}+...+\dfrac{1}{2021}-\)\(\dfrac{1}{2024}\)
=\(\dfrac{1}{4}-\dfrac{1}{2024}\)
=\(\dfrac{505}{2024}\)
N
3
O
25 tháng 3 2022
\(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}\)
\(=\dfrac{3\cdot1}{1\cdot4}+\dfrac{3\cdot1}{4\cdot7}+\dfrac{3\cdot1}{7\cdot10}+\dfrac{3\cdot1}{10\cdot13}+\dfrac{3\cdot3}{13\cdot16}\)
\(=3\cdot\left(\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+\dfrac{1}{10\cdot13}+\dfrac{1}{13\cdot16}\right)\)
\(=3\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right)\)
\(=3\cdot\left(1-\dfrac{1}{16}\right)\)
\(=3\cdot\left(\dfrac{16}{16}-\dfrac{1}{16}\right)\)
\(=3\cdot\dfrac{15}{16}\)
\(=\dfrac{45}{16}\)
3 tháng 5 2019
3/1.4+3/4.7+3/7.10+3/10.13
=1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13
=1 - 1/13
=12/13
MT
2
16 tháng 7 2015
3/1.4 + 3/4.7 + .. +3/13.16
= 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16
= 1/1 - 1/16
= 15/16
28 tháng 4 2018
1.
E = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{3}{7.10}\) + \(\dfrac{3}{10.13}\) + \(\dfrac{3}{13.16}\) + \(\dfrac{3}{16.19}\) + \(\dfrac{3}{19.22}\)
E = 1 - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{10}\) + ... +\(\dfrac{1}{19}\) - \(\dfrac{1}{22}\)
E = 1 - \(\dfrac{1}{22}\)
E = \(\dfrac{21}{22}\)
2.
(x - 4)(x - 5) = 0
TH1:
x - 4 = 0 => x = 4
TH2:
x - 5 = 0 => x = 5
Vậy: x = 4 hoặc x = 5
20 tháng 1 2018
3 x | x | - 24 x 73 = 2 x 74
3 x | x | - 24 = 2 x 74 : 73
3 x | x | - 24 = 2 x 7
3 x | x | - 16 = 14
3 x | x | = 14 + 16
3 x | x | = 30
| x | = 30 : 3
| x | = 10
\(\Rightarrow\)x = 10 ; - 10 ( thỏa mãn )
Vậy x = 10 ; -10
\(x+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{37.40}=\dfrac{-37}{40}\)
\(x+\left(\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{37.40}\right)=\dfrac{-37}{40}\)
\(x+\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{37}-\dfrac{1}{40}\right)=\dfrac{-37}{40}\)
\(x+\left(\dfrac{1}{4}-\dfrac{1}{40}\right)=\dfrac{-37}{40}\)
\(x+\dfrac{9}{40}=\dfrac{-37}{40}\)
\(x=\dfrac{-37}{40}-\dfrac{9}{40}\)
\(x=\dfrac{-23}{20}\)
Vậy ...
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