DT
1
K
Khách
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9 tháng 7 2018
\(a)\) \(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)
\(S=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)
\(3S=3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)
\(3S-S=\left(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\right)\)
\(2S=3+\frac{1}{3^7}\)
\(2S=\frac{3^8+1}{3^7}\)
\(S=\frac{3^8+1}{3^7}.\frac{1}{2}\)
\(S=\frac{3^8+1}{2.3^7}\)
Vậy \(S=\frac{3^8+1}{2.3^7}\)
Chúc bạn học tốt ~
S
1 tháng 11 2018
\(\frac{1}{2}\times\frac{1}{3}\times.........\times\frac{1}{10}=\frac{1}{2\times3}+......+\frac{1}{9\times10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-..........-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
HP
1
18 tháng 8 2015
\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+...+\frac{1}{8}\times\frac{1}{9}=\frac{1}{2\times3}+\frac{1}{3\times4}+....+\frac{1}{8\times9}\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)
K4
0
LM
Lê Minh Vũ
VIP
7 tháng 7 2023
\(4,7\div0,25+5,3\times4\)
\(=18,8+21,2\)
\(=40\)
\(3\times\left(a-2\right)+150=240\)
\(3\times\left(a-2\right)=90\)
\(a-2=30\)
\(a=32\)
\(\dfrac{1}{9}+a+\dfrac{7}{12}=\dfrac{17}{18}\)
\(\dfrac{1}{9}+a=\dfrac{13}{36}\)
\(a=\dfrac{1}{4}\)
\(\left(\dfrac{1}{2}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}+\dfrac{1}{4}\times\dfrac{1}{5}+\dfrac{1}{5}\times\dfrac{1}{6}+\dfrac{1}{6}\times\dfrac{1}{7}+\dfrac{1}{7}\times\dfrac{1}{8}\right)\times a=\dfrac{9}{16}\)
\(\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}\right)\times a=\dfrac{9}{16}\)
\(\left(\dfrac{1}{2}-\dfrac{1}{8}\right)\times a=\dfrac{9}{16}\)
\(\dfrac{3}{8}\times a=\dfrac{9}{16}\)
\(a=\dfrac{3}{2}\)
TT
20 tháng 7 2020
\(E=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)....\left(1-\frac{1}{2006}\right)\left(1-\frac{1}{2007}\right)\)
\(E=\frac{1}{2}.\frac{2}{3}....\frac{2005}{2006}.\frac{2006}{2007}\)
\(E=\frac{1.2.3.4...2005.2006}{2.3.4.5....2006.2007}\)
\(E=\frac{1}{2007}\)
TT
5
6 tháng 9 2016
( 1/2 + 1/3 + 1/4 + 1/5 + ... + 1/10 ) . x = 1/9 + 2/8 + 3/7 + ...+ 9/1
( 1/2 + 1/3 + 1/4 + 1/5 + ... + 1/10 ) . x = 19,28968264
1,928968254 .x = 19,28968264
x=19,28968264:1,928968254
x=10,0000000518412
6 tháng 9 2016
giờ mình mới biết
( 1/2 + 1/3 + 1/4 + ... + 1/10 ) . x = 1/9 + 2/8 + ... + 9/1
=> x = ( 1/9 + 2/8 + ... + 9/1 ) : ( 1/2 + 1/3 + ... 1/10 )
=> x = ( 9/1 + 8/2 + ... + 2/8 + 1/9 ) : ( 1/2 + 1/3 + 1/4 + ... + 1/10 )
=>x = [ ( 9 - 1 - 1 -... - 1 ) +( 8/2 + 1 ) + ( 7/3 + 1 ) + ... + ( 1/9 + 1 ) ] : ( 1/2 + 1/3 + 1/4 + ... + 1/10 )
=> x = ( 1 + 10/2 + 10/3 + ... + 10/9 ) : ( 1/2 + 1/3 + 1/4 + ... + 1/10 )
=> x = [10 . ( 1/2 + 1/3 + ... + 1/9 ) ] : ( 1/2 + 1/3 + 1/4 + ... + 1/10 )
=> x = 10
A = ( 1 - \(\dfrac{1}{2}\)) \(\times\)( 1 - \(\dfrac{1}{3}\)) \(\times\) ( 1 - \(\dfrac{1}{4}\)) \(\times\)...\(\times\) ( 1 - \(\dfrac{1}{8}\)) \(\times\) ( 1 - \(\dfrac{1}{9}\))
A = \(\dfrac{1}{2}\) \(\times\) \(\dfrac{2}{3}\) \(\times\) \(\dfrac{3}{4}\) \(\times\)...\(\times\) \(\dfrac{7}{8}\) \(\times\) \(\dfrac{8}{9}\)
A = \(\dfrac{1}{9}\) \(\times\) \(\dfrac{2\times3\times...\times7\times8}{2\times3\times...\times7\times8}\)
A = \(\dfrac{1}{9}\)