\(\left(\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{17\times19}\right)\times114-0,2\left(x-1\right)=10\)
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LK
4
TM
17 tháng 7 2016
Đặt \(A=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{17x19}\)
=>\(2xA=2x\left(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{17x19}\right)\)
=>\(2xA=\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{17x19}\)
=>\(2xA=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\)
=>\(2xA=1-\frac{1}{19}=\frac{18}{19}\)
=>\(A=\frac{18}{19}:2=\frac{9}{19}\)
NT
17 tháng 7 2016
(\(\frac{1}{1}-\frac{1}{3}\left(\right)+\left(\right)\frac{1}{3}-\frac{1}{5}\left(\right)+\left(\right)\frac{1}{5}-\frac{1}{7}\left(\right)+....+\left(\right)\frac{1}{17}-\frac{1}{19}\left(\right)\)\(\frac{1}{19}\)
\(\frac{1}{1}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+....+\left(\frac{1}{17}-\frac{1}{17}\right)-\frac{1}{19}\)
\(\frac{1}{1}-\frac{1}{19}=\frac{18}{19}\)
9 tháng 8 2016
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)
\(2.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{\left(2x+1\right).\left(2x+3\right)}\right)=2.\frac{15}{93}\)
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{\left(2x+1\right).\left(2x+3\right)}=\frac{10}{31}\)
\(\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)
\(\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)
\(\frac{1}{2x+3}=\frac{1}{93}\)
\(\Rightarrow2x+3=93\)
\(\Rightarrow2x=90\)
\(\Rightarrow x=45\)
8 tháng 8 2016
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{96}\)
\(2.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}\right)=2.\frac{15}{96}\)
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{\left(2x+1\right).\left(2x+3\right)}=\frac{5}{16}\)
\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}=\frac{5}{16}\)
\(\frac{1}{3}-\frac{1}{2x+3}=\frac{5}{16}\)
\(\frac{1}{2x+3}=\frac{1}{3}-\frac{5}{16}\)
\(\frac{1}{2x+3}=\frac{1}{48}\)
=> 2x + 3 = 48
=> 2x = 48 - 3
=> 2x = 45
=> x = 45/2
21 tháng 8 2015
1=3/3=4/4=5/5=...
=> 1+1/1*3=3/1*3=1/1
=> 1+1/2*4=4/2*4=1/2
=>...
Bieu thuc se con lai la 1*1/2*1/3*1/4*1/5
Vay A=1/120
3 tháng 6 2015
(4/1*3+4/3*5+4/5*7+4/7*9)*10-x=0
=4*2/1*3+4*2/3*5+4*2/5*7+4*2/7*9
=1/1+1/3+1/5+1/7+1/9
=1/1-1/9
=8/9
8/9*10-x=0
89-x=0
x=89-0
x=89
27 tháng 1 2017
a)\(VT=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+...+\frac{1}{\left(3n-1\right)\left(3n+2\right)}\)
\(=\frac{1}{3}\left[\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+...+\frac{3}{\left(3n-1\right)\left(3n+2\right)}\right]\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{3n-1}-\frac{1}{3n+2}\)
\(=\frac{1}{2}-\frac{1}{3n+2}=\frac{3n+2}{2\cdot\left(3n+2\right)}-\frac{2}{2\cdot\left(3n+2\right)}\)
\(=\frac{3n+2-2}{6n+4}=\frac{3n}{6n+4}=VP\)
27 tháng 7 2015
\(\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\right)\times y=\frac{2}{3}\)
\(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\times y=\frac{2}{3}\)
\(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{11}\right)\times y=\frac{2}{3}\)
\(\frac{1}{2}\times\frac{10}{11}\times y=\frac{2}{3}\)
\(\frac{5}{11}\times y=\frac{2}{3}\) => \(y=\frac{2}{3}:\frac{5}{11}=\frac{2}{3}\times\frac{11}{5}=\frac{22}{15}\)
\(\left(\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{17\times19}\right)\times114-0,2\left(x-1\right)=10\)
\(\Rightarrow\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\right)\right]\times114-0,2x+0,2=10\)
\(\Rightarrow\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{19}\right)\right]\times114+0,2-0,2x=10\)
\(\Rightarrow\frac{8}{57}\times114+0,2-0,2x=10\Rightarrow16+0,2-0,2x=10\)
\(\Rightarrow16,2-0,2x=10\Rightarrow0,2x=16,2-10\Rightarrow0,2x=6,2\Rightarrow x=31\)