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=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:
\(A=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{15\left(x+3\right)}=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{303}{308}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{305-2}{305+3}\\ \Rightarrow x=305\)
\(\dfrac{13+x}{20}\) = \(\dfrac{3}{4}\)
13 + \(x\) = 20 \(\times\) \(\dfrac{3}{4}\)
13 + \(x\) = 15
\(x\) = 15 - 13
\(x\) = 2
Cách khác :
\(\dfrac{13+x}{20}=\dfrac{3}{4}\)
\(\dfrac{13+x}{20}=\dfrac{15}{20}\)
\(13+x=15\)
\(x=15-13\)
\(x=2\)
\(\frac{7}{3}:\frac{5}{x}=\frac{14}{15}\)
\(\frac{5}{x}=\frac{7}{3}:\frac{14}{15}\)
\(\frac{5}{x}=\frac{5}{2}\)=> x = 2
\(\frac{7}{3}:\frac{5}{x}=\frac{14}{15}\)
\(\Rightarrow\frac{5}{x}=\frac{7}{3}:\frac{14}{15}\)
\(\Rightarrow\frac{5}{x}=\frac{5}{2}\)
\(\Rightarrow x=2\)
Vậy x = 2
_Chúc bạn học tốt_
a) \(\frac{21\times11\times2\times17\times4}{11\times17\times21\times3}=\frac{2\times4}{3}_{ }=\frac{8}{3}\)
b)\(\frac{5\times7\times13\times2}{7\times2\times13\times5\times5}=\frac{1}{5}\)
a)\(\frac{21x22x68}{11x17x63}\) = \(\frac{1x2x4}{1x1x3}\) =\(\frac{8}{3}\)
b)\(\frac{5x7x26}{14x13x25}\) = \(\frac{1x1x2}{2x1x5}\) =\(\frac{1x1x1}{1x1x5}\) = \(\frac{1}{5}\)
`#3107`
`7/13 \div x = 14/39`
`=> x = 7/13 \div 14/39`
`=> x = 3/2`
Vậy, `x = 3/2`
________
`x \times 3/5 = 14/15`
`=> x = 14/15 \div 3/5`
`=> x = 14/9`
Vậy, `x=14/9.`
\(\dfrac{7}{13}:x=\dfrac{14}{39}\)
\(x=\dfrac{7}{13}:\dfrac{14}{39}\)
\(x=\dfrac{7}{13}\times\dfrac{39}{14}\)
\(x=\dfrac{3}{2}\)
___
\(x\times\dfrac{3}{5}=\dfrac{14}{15}\)
\(x=\dfrac{14}{15}:\dfrac{3}{5}\)
\(x=\dfrac{14}{15}\times\dfrac{5}{3}\)
\(x=\dfrac{14}{9}\)