1/ 2 + 1/6 + 1/ 12 + 1/20 = y /20
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\(y-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}=1\)
\(y-\frac{210}{420}-\frac{70}{420}-\frac{35}{420}-\frac{21}{420}-\frac{14}{430}-\frac{10}{420}=1\)
\(y-\frac{210-70-35-21-14-10}{420}=1\)
\(y-\frac{60}{420}=1\)
\(y-\frac{1}{7}=1\)
\(y=1+\frac{1}{7}\)
\(y=\frac{7}{7}+\frac{1}{7}\)
\(y=\frac{8}{7}\)
(y - 1/2) : (1/2 + 1/6 + 1/12 + ... + 1/90) = 1/3
(y - 1/2) : (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/9×10) = 1/3
(y - 1/2) : (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10) = 1/3
(y - 1/2) : (1 - 1/10) = 1/3
(y - 1/2) : 9/10 = 1/3
y - 1/2 = 1/3 × 9/10
y - 1/2 = 3/10
y = 3/10 + 1/2
y = 3/10 + 5/10
y =8/10 = 4/5
(y - \(\dfrac{1}{2}\)) : \(\left(\dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\right)\)= \(\dfrac{1}{3}\)
(y\(-\dfrac{1}{2}\)): \(\left(\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)= \(\dfrac{1}{3}\)
\(\left(y-\dfrac{1}{2}\right):\left(\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{10}\right)=\dfrac{1}{3}\)
\(\left(y-\dfrac{1}{2}\right):\dfrac{3}{10}=\dfrac{1}{3}\)
\(\left(y-\dfrac{1}{2}\right)=\dfrac{1}{10}\)
y = \(\dfrac{3}{5}\)
\(y\times\dfrac{1}{2}+y\times\dfrac{1}{6}+y\times\dfrac{1}{12}+y\times\dfrac{1}{20}=\dfrac{8}{5}\)
\(y\times\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}\right)=\dfrac{8}{5}\)
\(y\times\dfrac{4}{5}=\dfrac{8}{5}\)
\(\dfrac{8}{5}:\dfrac{4}{5}\)
\(y=\dfrac{8}{4}=2\)
Y - 1/2 - 1/6 - 1/12 - 1/20 - 1/30 - 1/42 = 1
Đặt A= - 1/2 - 1/6 - 1/12 - 1/20 - 1/30 - 1/42
\(A=-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}\right)\)
\(A=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{6.7}\right)\)
\(A=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=-\left(1-\frac{1}{7}\right)\)
\(A=-\frac{6}{7}\).Thay A vào ta có \(Y-\frac{6}{7}=1\Leftrightarrow y=\frac{13}{7}\)
1/ 2 + 1/6 + 1/ 12 + 1/20 = y /20
4/5=y/20
5.y=20.4
5.y=80
y=16
1/2 + 1/6 + 1/12 + 1/20
10/20 + 2/12 + 1/12 + 1/20
11/20 + 3/12
11/20 + 1/4
11/20 + 5/20 = 4/5