1.4x - 3.2x = 2.5 - 4.5
✳ LƯU Ý : DẤU CHẤM LÀ DẤU NHÂN NHÉ !
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MN
7 tháng 6 2021
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+.......+\dfrac{1}{x\cdot\left(x+1\right)}=\dfrac{122}{123}\)
\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{122}{123}\)
\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{122}{123}\)
\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{123}\)
\(\Leftrightarrow x=122\)
TY
2 tháng 3 2017
1)
A= \(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{39.40}\)
\(\Rightarrow A=\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-...+\frac{1}{39}-\frac{1}{40}\)
\(\Rightarrow A=\frac{1}{3}-\frac{1}{40}\)
=> A= 27/120
S
2 tháng 3 2017
A = \(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{39.40}\)
= \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{39}-\frac{1}{40}\)
= \(\frac{1}{3}-\frac{1}{40}\)
= \(\frac{37}{120}\)
B = \(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{37.40}\)
= \(\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{37}-\frac{1}{40}\right)\)
= \(\frac{1}{3}\left(\frac{1}{4}-\frac{1}{40}\right)\)
= \(\frac{1}{3}.\frac{9}{40}=\frac{3}{40}\)
C = \(\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{37.40}\)
= \(\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{37}-\frac{1}{40}\right)\)
= \(\frac{2}{3}.\left(\frac{1}{4}-\frac{1}{40}\right)\)
= \(\frac{2}{3}.\frac{9}{40}=\frac{3}{20}\)
29 tháng 5 2019
\(\frac{2}{5}.\frac{1}{x}+\frac{1}{x}.2+\frac{2}{5}=0,5\)
\(\Rightarrow\frac{2}{5x}+\frac{2}{x}+\frac{2}{5}=\frac{1}{2}\)
\(\Rightarrow2.\left(\frac{1}{5x}+\frac{1}{x}+\frac{1}{5}\right)=\frac{1}{2}\)
\(\Rightarrow\frac{1}{5x}+\frac{5}{5x}+\frac{x}{5x}=\frac{1}{2}:2=\frac{1}{4}\)
\(\Rightarrow\frac{1+5+x}{5x}=\frac{1}{4}\)
\(\Rightarrow4.\left(1+5+x\right)=5x\)
\(\Rightarrow4+20+4x=5x\)
\(\Rightarrow24+4x=5x\)
\(\Rightarrow5x-4x=24\)
\(\Rightarrow x=24\)
TT
4
6 tháng 6 2017
\(\frac{7256.4375-725}{3650+4375.7255}\)
\(=\frac{\left(7255+1\right).4375-725}{3650+4375.7255}\)
\(=\frac{7255.4375+4375-725}{3650+4375.7255}\)
\(=\frac{7255.4375+3650}{3650+4375.7255}\)
\(=1\)
12 tháng 9 2020
43.17+29.57+13.43+57
=43.(17+13)+57.(29+1)
=43.30+57.30
=30.(43+57)
=30.100=3000
12 tháng 9 2020
\(43.17+29.57+13.43+57\)
\(=43.\left(17+13\right)+57.\left(29+1\right)\)
\(\text{= 43.30 + 57.30}\)
\(=30.\left(47+57\right)\)
\(=30.100\)
\(=3000\)
Hok tốt !
TK
0
NH
20 tháng 7 2016
\(a,A=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+...+\frac{3}{90}\)
\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=3.\left(1-\frac{1}{10}\right)\)
\(A=3.\frac{9}{10}=\frac{27}{10}\)
\(b,B=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(B.\frac{3}{2}=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{17}\)
\(B=\frac{15}{34}:\frac{3}{2}=\frac{5}{17}\)
Ta suy ra:
4x-6x = 10-20
=> -2x = -10
=> x= -10/-2 = 5
Vay: x=5