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NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
8 tháng 4 2023
A = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\)+.....+ \(\dfrac{1}{105}\)
A \(\times\) \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) +.....+ \(\dfrac{1}{105}\))
A \(\times\) \(\dfrac{1}{2}\) = \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+.....+ \(\dfrac{1}{210}\)
A \(\times\) \(\dfrac{1}{2}\) = \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\)+ \(\dfrac{1}{4\times5}\)+....+\(\dfrac{1}{14\times15}\)
A \(\times\) \(\dfrac{1}{2}\) = \(\dfrac{1}{2}-\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)+.....+ \(\dfrac{1}{14}\) - \(\dfrac{1}{15}\)
A \(\times\) \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\) - \(\dfrac{1}{15}\)
A \(\times\) \(\dfrac{1}{2}\) = \(\dfrac{13}{30}\)
A = \(\dfrac{13}{30}\) : \(\dfrac{1}{2}\)
A = \(\dfrac{13}{15}\)
AH
0
TT
1
MA
30 tháng 3 2016
nhân 2 vế với 1/2 ta có
1/2 x A = 1/2 x (1/3 + 1/6 +1/10 + 1/15 + .......+1/91 + 1/105 )
1/2 x A = 1/6 +1/12 + 1/20 + 1/30 + ...............+1/182 + 1/210
1/2 x A = 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) +................+1/(13x14) + 1/(14x15)
1/2 x A = 1/2 - 1/3 +1/3 -1/4 + 1/4 - 1/5 +1/5 - 1/6+.........+1/13 - 1/14 + 1/14 - 1/15
1/2 x A = 1/2 - 1/15 =13/30
=> A = 13/30 : 1/2=13/15 <1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
13 tháng 4 2023
P = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\)+.....+ \(\dfrac{1}{105}\)
P = \(\dfrac{2}{2}\) \(\times\) ( \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\)+ ......+ \(\dfrac{1}{105}\))
P = 2 \(\times\) ( \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+......+ \(\dfrac{1}{210}\))
P = 2 \(\times\) ( \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\) + \(\dfrac{1}{4\times5}\)+.....+\(\dfrac{1}{14\times15}\))
P = 2 \(\times\) ( \(\dfrac{1}{2}-\dfrac{1}{3}\) + \(\dfrac{1}{3}-\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) +......+ \(\dfrac{1}{14}\) - \(\dfrac{1}{15}\))
P = 2 \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{15}\))
P = 2 \(\times\) \(\dfrac{13}{30}\)
P = \(\dfrac{13}{15}\)
DN
3
LH
1
25 tháng 2
a: \(\left(\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}\right):\left(\dfrac{1}{6}+\dfrac{1}{10}-\dfrac{1}{15}\right)\)
\(=\dfrac{5+3+2}{30}:\dfrac{5+3-2}{30}\)
\(=\dfrac{10}{30}\cdot\dfrac{30}{6}\)
\(=\dfrac{10}{6}=\dfrac{5}{3}\)
b: \(\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{5}\right):\left(\dfrac{1}{4}-\dfrac{1}{6}\right)\)
\(=\dfrac{30-20+15-12}{60}:\dfrac{3-2}{12}\)
\(=\dfrac{13}{60}\cdot\dfrac{12}{1}=\dfrac{13}{5}\)
VH
3
1 tháng 9 2016
\(\frac{\frac{1}{6}+\frac{1}{10}+\frac{1}{15}}{\frac{1}{6}+\frac{1}{10}-\frac{1}{15}}=\frac{\frac{5+3+2}{30}}{\frac{5+3-2}{30}}=\frac{\frac{1}{3}}{\frac{1}{5}}=1\frac{2}{3}\)
\(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{1}{4}-\frac{1}{6}}=\frac{\frac{30-20+15-12}{60}}{\frac{3-2}{12}}=\frac{\frac{13}{60}}{\frac{1}{12}}=2\frac{3}{5}\)
tíc nha mn, mình đang bị âm điểm
C
12 tháng 3 2022
1/1 - 1/12= 12/12 - 1/12= 11/12
15/1 - 3/4= 60/4 - 3/4= 57/4
1/1 - 1/10= 10/10 - 1/10= 9/10
5/1 - 3/5= 25/5 - 3/5= 22/5
N
12 tháng 3 2022
\(1-\dfrac{1}{12}=\dfrac{12}{12}-\dfrac{1}{12}=\dfrac{11}{12}\)
\(15-\dfrac{3}{4}=\dfrac{60}{4}-\dfrac{3}{4}=\dfrac{57}{4}\)
\(1-\dfrac{1}{10}=\dfrac{10}{10}-\dfrac{1}{10}=\dfrac{9}{10}\)
\(5-\dfrac{15}{25}=\dfrac{125}{25}-\dfrac{15}{25}=\dfrac{110}{25}=\dfrac{22}{5}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{105}\)
=\(\frac{2}{6}+\frac{2}{12}+\frac{1}{20}+.....+\frac{2}{210}\)
= \(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{14.15}\right)\)
= \(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{14}-\frac{1}{15}\right)\)
= \(2\left(\frac{1}{2}-\frac{1}{15}\right)\)
= 2 . \(\frac{13}{30}\)
= \(\frac{13}{15}\)