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\(y-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}=1\)
\(y-\frac{210}{420}-\frac{70}{420}-\frac{35}{420}-\frac{21}{420}-\frac{14}{430}-\frac{10}{420}=1\)
\(y-\frac{210-70-35-21-14-10}{420}=1\)
\(y-\frac{60}{420}=1\)
\(y-\frac{1}{7}=1\)
\(y=1+\frac{1}{7}\)
\(y=\frac{7}{7}+\frac{1}{7}\)
\(y=\frac{8}{7}\)
\(x-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\right)=1\)
\(x-\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{5\times4}+\dfrac{1}{5\times6}+\dfrac{1}{7\times6}\right)=1\)
\(x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)=1\)
\(x-\left(1-\dfrac{1}{7}\right)=1\)
\(x-1+\dfrac{1}{7}=1\)
\(x+\dfrac{1}{7}=1+1\)
\(x+\dfrac{1}{7}=2\)
\(x=2-\dfrac{1}{7}\)
\(x=\dfrac{14-1}{7}=\dfrac{13}{7}\)
Nguyễn Ngọc Ánh: nhầm dấu hơi nhìu nhưng c.ơn đã giải cho mik.
=15/30+5/30+1/12+1/20+1/30+1/42
=2/3+1/12+1/20+1/30+1/42
=8/12+1/12+1/20+1/30+1/42
=3/4+1/20+1/30+1/42
=15/20+1/20+1/30+1/42
=4/5+1/30+1/42
=24/30+1/30+1/42
=5/6+1/42
=35/42+1/42
=6/7
A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
A=\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
A=\(1-\frac{1}{7}\)
A=\(\frac{6}{7}\)
=(1/1-1/2)+(1/2-1/3)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7) =(1/2-1/2)+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)+(1/1-1/7) = 0+0+0+0+0+6/7 =6/7
\(M=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{6.7}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{6}-\dfrac{1}{7}=1-\dfrac{1}{7}=\dfrac{6}{7}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{6\times7}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}=1-\frac{1}{7}=\frac{6}{7}\)
\(\frac{1}{2} +\frac{1}{6}+\frac{1}{21}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{23}{28}\)
Gọi tổng trên là A
A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7
A = 1 - 1/2 + 1/2 - 1/3 +.......+ 1/6 - 1/7
A = 1 - 1/7
A = 6/7
1/2+1/6+1/12+1/20+1/30+1/42
=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7=7-1/7=6/7
1/42 + 1/30 + 1/20 + 1/12 + 1/6 + 1/2
= 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7
= 1 - 1/7
= 6/7
Chú ý : Dấu " . " là dấu x
x + 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 = 1
x + 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 = 1
x + 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 = 1
x + 1/1 - 1/7 = 1
x + 6/7 = 1
x = 1 - 6/7
x = 1/7
x + 1/2 + 1/6 + 1/20 + 1/30 + 1/42 = 1
x + 65/84 = 1
x = 1 - 65/84
x = 19/84