\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+.............+\frac{3}{418}+\frac{3}{550}\).
K
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T
10 tháng 7 2015
= \(\frac{9}{1x4}+\frac{9}{4x7}+\frac{9}{7x10}+.........+\frac{9}{19x22}+\frac{9}{22x25}\)
= \(\frac{1}{3}x\left(\frac{9}{1}-\frac{9}{4}\right)+\left(\frac{9}{4}-\frac{9}{7}\right)x\frac{1}{3}+........+\left(\frac{9}{22}-\frac{9}{25}\right)x\frac{1}{3}\)
= \(\frac{1}{3}\left(\frac{9}{1}-\frac{9}{4}+\frac{9}{4}-\frac{9}{7}+....+\frac{9}{22}-\frac{9}{25}\right)\)
= \(\frac{1}{3}x\left(\frac{9}{1}-\frac{9}{25}\right)\)
= \(\frac{1}{3}x\frac{216}{25}\)
= \(\frac{72}{25}\)
nhớ ********** nha bn thân
10 tháng 7 2015
\(\frac{9}{4}+\frac{9}{28}+\frac{9}{70}+\frac{9}{130}+...+\frac{9}{418}+\frac{9}{550}\)
\(=3\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{19.22}+\frac{3}{22.25}\right)\)
\(=3\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{25}\right)\)
\(=3\left(1-\frac{1}{25}\right)\)
\(=3.\frac{24}{25}=\frac{72}{25}\)
M
16 tháng 1 2016
a) \(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}+\frac{3}{418}+\frac{3}{550}\)
= \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}+\frac{3}{19.22}+\frac{3}{22.25}\)
= \(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}+\frac{1}{19}-\frac{1}{22}+\frac{1}{22}-\frac{1}{25}\)
= \(\frac{1}{1}-\frac{1}{25}\)
= \(\frac{24}{25}\)
b) \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{\left(2n+1\right).\left(2n+3\right)}\)
= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2n+1}-\frac{1}{2n+3}\)
= \(\frac{1}{1}-\frac{1}{2n+3}\)
= \(\frac{2n+2}{2n+3}\)
c) \(\frac{7+\frac{7}{13}-\frac{7}{48}+\frac{7}{95}}{15+\frac{15}{13}-\frac{15}{48}+\frac{15}{95}}-\frac{7070707}{15151515}\)
= \(\frac{7\left(1+\frac{1}{13}-\frac{1}{48}+\frac{1}{95}\right)}{15\left(1+\frac{1}{13}-\frac{1}{48}+\frac{1}{95}\right)}-\frac{7.1010101}{15.1010101}\)
= \(\frac{7}{15}-\frac{7}{15}\)
= 0
9 tháng 7 2015
Đặt A = 9/4 + 9/28 +.. + 9/550
A = 9/1.4 + 9/4.7 +... + 9/22.25
A = 3( 3/1.4 + 3/4.7 + .. + 3/22.25)
A = 3 . (1/1 - 1/4 + 1/4 - 1/7 + ... +1/22 - 1/25)
A = 3 (1 - 1/25)
A = 3. 24 / 25
A = 72/25
6 tháng 1 2017
Lướt qua rồi! không phải bạn k mà ấn tượng "đừng lướt qua"
\(A=\frac{3a}{4.1}+\frac{3a}{7.4}+\frac{3a}{10.7}+\frac{3a}{13.10}+..+\frac{3a}{22.19}+\frac{3a}{25.22}=\frac{48}{25}\)
\(a.\left(\frac{3}{4.1}+\frac{3}{7.4}+\frac{3}{10.7}+\frac{3}{13.10}+..+\frac{3}{22.19}+\frac{3}{25.22}\right)=\frac{48}{25}\)
\(B=\left(\frac{3}{4.1}+\frac{3}{7.4}+\frac{3}{10.7}+\frac{3}{13.10}+..+\frac{3}{22.19}+\frac{3}{25.22}\right)\)
\(B=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+..+\frac{1}{22}-\frac{1}{25}\)
\(B=\frac{1}{1}-\frac{1}{25}=\frac{24}{25}\)
\(A=a.B=\frac{24a}{25}=\frac{48}{25}\Rightarrow a=2\)
6 tháng 1 2017
\(\frac{3a}{4}+\frac{3a}{28}+\frac{3a}{70}+...+\frac{3a}{418}+\frac{3a}{550}=\frac{48}{25}\)
\(\Rightarrow a\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{19.22}+\frac{3}{22.25}\right)=\frac{48}{25}\)
\(\Rightarrow a\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}+\frac{1}{22}-\frac{1}{25}\right)=\frac{48}{25}\)
\(\Rightarrow a\left(1-\frac{1}{25}\right)=\frac{48}{25}\)
\(\Rightarrow a.\frac{24}{25}=\frac{48}{25}\)
\(\Rightarrow a=2\)
TN
0
DD
4 tháng 8 2015
\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)
\( B=\frac{1}{2}-\frac{1}{14}=\frac{3}{7}\)
\(C=\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\)
\(C=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\)
\(C=\frac{1}{1}-\frac{1}{16}=\frac{15}{16}\)
10 tháng 9 2017
b) D = \(\frac{3}{4}+\frac{3}{8}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)
D = \(3\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208}+\frac{1}{304}\right)\)
D = \(3\left(\frac{1}{1x4}+\frac{1}{4x7}+\frac{1}{7x10}+\frac{1}{10x13}+\frac{1}{13x16}+\frac{1}{16x19}\right)\)
D = \(\frac{1}{1}-\frac{1}{19}=\frac{18}{19}\)
Chắc vậy
PQ
3
30 tháng 7 2020
\(3\times\left(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+\frac{x}{130}\right)=\frac{60}{13}\)
=> \(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+\frac{x}{130}=\frac{20}{13}\)
=> \(\frac{x}{1\cdot4}+\frac{x}{4\cdot7}+\frac{x}{7\cdot10}+\frac{x}{10\cdot13}=\frac{20}{13}\)
=> \(\frac{x}{3}\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}\right)=\frac{20}{13}\)
=> \(\frac{x}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{10}-\frac{1}{13}\right)=\frac{20}{13}\)
=> \(\frac{x}{3}\left(1-\frac{1}{13}\right)=\frac{20}{13}\)
=> \(\frac{x}{3}\cdot\frac{12}{13}=\frac{20}{13}\)
=> \(\frac{x}{3}=\frac{20}{13}:\frac{12}{13}=\frac{20}{13}\cdot\frac{13}{12}=\frac{5}{3}\)
=> x = 5
30 tháng 7 2020
\(3\cdot\left(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+\frac{x}{130}\right)=\frac{60}{13}\)
\(3\cdot\left(\frac{x}{1\cdot4}+\frac{x}{4\cdot7}+\frac{x}{7\cdot10}+\frac{x}{10\cdot13}\right)=\frac{60}{13}\)
\(3\left(x-3\right)\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}\right)=\frac{60}{13}\)
\(\left(3x-9\right)\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}\right)=\frac{60}{13}\)
\(\left(3x-9\right)\left(1-\frac{1}{13}\right)=\frac{60}{13}\)
\(\left(3x-9\right)\cdot\frac{12}{13}=\frac{60}{13}\)
\(3x-9=\frac{\frac{60}{13}}{\frac{12}{13}}\)
\(3x-9=5\)
\(3x=5+9\)
\(3x=14\)
\(x=\frac{14}{3}\approx4,667\)
12 tháng 8 2018
A = \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{7.8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
B = \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(=1-\frac{1}{13}=\frac{12}{13}\)
19 tháng 3 2019
\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{7.8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
\(B=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(=1-\frac{1}{13}=\frac{12}{13}\)
\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+....+\frac{3}{418}+\frac{3}{550}\)
\(\Leftrightarrow\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{19.22}+\frac{3}{22.25}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{22}+\frac{1}{22}-\frac{1}{25}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{25}=\frac{24}{25}\)
Nhớ k cho m nhé!