=13/12x14/13x15/14x16/15x...x2006/2005x2007/2006x2008/2007

=2008/12

=502/3

A = 1\(\dfrac{1}{12}\) \(\times\) 1\(\dfrac{1}{13}\) \(\times\) 1\(\dfrac{1}{14}\) \(\times\) 1\(\dfrac{1}{15}\) \(\times\) ... \(\times\) 1\(\dfrac{1}{2005}\) \(\times\) 1\(\dfrac{1}{2006}\) \(\times\) 1\(\dfrac{1}{2007}\)

A = ( 1 + \(\dfrac{1}{12}\)) \(\times\) ( 1 + \(\dfrac{1}{13}\)) \(\times\) ( 1 + \(\dfrac{1}{14}\)) \(\times\)...\(\times\) ( 1 + \(\dfrac{1}{2006}\))\(\times\)(1+\(\dfrac{1}{2007}\))

A = \(\dfrac{13}{12}\) \(\times\) \(\dfrac{14}{13}\) \(\times\) \(\dfrac{15}{14}\) \(\times\) ...\(\times\) \(\dfrac{2007}{2006}\) \(\times\) \(\dfrac{2008}{2007}\)

A = \(\dfrac{13\times14\times15\times...\times2007}{13\times14\times15\times...\times2007}\) \(\times\) \(\dfrac{2008}{12}\)

A = 1 \(\times\) \(\dfrac{502}{3}\)

A = \(\dfrac{502}{3}\)

Ta có công thức tổng quát: 

\(\dfrac{k}{n\cdot\left(n+k\right)}=\dfrac{1}{n}-\dfrac{1}{n+k}\)

\(a,A=\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}\\ =\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\left(\dfrac{1}{5}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\dfrac{x-2}{5\left(x+3\right)}\\ =\dfrac{x-2}{15\left(x+3\right)}\)

Theo đề bài ta có: 

\(A=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{15\left(x+3\right)}=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{303}{308}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{305-2}{305+3}\\ \Rightarrow x=305\)

khó nhỉ

 \(\dfrac{13+x}{20}\) = \(\dfrac{3}{4}\)

    13 + \(x\)  = 20 \(\times\) \(\dfrac{3}{4}\)

     13 + \(x\) = 15 

              \(x\) = 15 - 13

                \(x\) = 2

Cách khác :

\(\dfrac{13+x}{20}=\dfrac{3}{4}\)

\(\dfrac{13+x}{20}=\dfrac{15}{20}\)

\(13+x=15\)

\(x=15-13\)

\(x=2\)

\(71+52,5\times4=\frac{x+140}{x}+210\)

\(71+210=\frac{x+140}{x}+210\)

\(=>\frac{x+140}{x}=71\)

\(71=\frac{142}{2}\)\(\Rightarrow x=142-140=2\)

a) \(38,7\times\left(38,7-x\right)=38,7\)

\(38,7-x=38,7:38,7\)

\(38,7-x=1\)

\(x=38,7-1\)

\(x=37,7\)

De phan b) co bi nham khong ban ^.^

Bn lớp 5 suy nghĩ đi chứ

Lớp 4 học rồi 

dễ thế mà

BẠN LẤY CÁI 5/30+45/270 NHA

NHỚ K NHA

a) \(\frac{1}{2}\times x-3=6\)

=> \(\frac{1}{2}\times x=6+3\)

=> \(\frac{1}{2}\times x=9\)

=>\(x=9:\frac{1}{2}\)

=> \(x=18\)

b) \(2:x=\frac{2}{5}--\frac{1}{10}\)

=> \(2:x=\frac{2}{5}+\frac{1}{10}\)

=> \(2:x=\frac{1}{2}\)

=> \(x=2:\frac{1}{2}\)

=> \(x=4\)

c) \(25-\left(2\frac{1}{2}+x\right)=10\)

=> \(2\frac{1}{2}+x=25-10\)

=> \(\frac{5}{2}+x=15\)

=>\(x=15-\frac{5}{2}\)

=> \(x=\frac{25}{2}\)

d) \(\left(x-\frac{3}{4}\right)\times3-45:9=10\)

=> \(\left(x-\frac{3}{4}\right)\times3-5=10\)

=> \(\left(x-\frac{3}{4}\right)\times3=10+5\)

=> \(\left(x-\frac{3}{4}\right)\times3=15\)

=> \(\left(x-\frac{3}{4}\right)=15:3\)

=> \(\left(x-\frac{3}{4}\right)=5\)

=> \(x=5+\frac{3}{4}\)

=> \(x=\frac{23}{4}\)

\(a,\frac{1}{2}.x-3=6\Rightarrow\frac{x}{2}=9\Rightarrow x=18\)

\(b,2:x=\frac{2}{5}-\frac{1}{10}\Rightarrow\frac{2}{x}=\frac{9}{10}\Rightarrow x=\frac{2.10}{9}=\frac{20}{9}\)

\(c,25-\left(2\frac{1}{2}+x\right)=10\Rightarrow25-\frac{5}{2}+x=10\Rightarrow x=10+\frac{5}{2}-25=-\frac{25}{2}\)

\(d,\left(x-\frac{3}{4}\right).3-45:9=10\Rightarrow\left(x-\frac{3}{4}\right).3-5=10\Rightarrow\left(x-\frac{3}{4}\right).3=15\Rightarrow x-\frac{3}{4}=5\Rightarrow x=\frac{23}{4}\)