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#)Giải :
\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-\frac{19}{45}+...-\frac{119}{4950}\)
\(S=\frac{38}{25}+\left(\frac{9}{10}-\frac{11}{15}\right)+\left(\frac{13}{21}-\frac{15}{28}\right) +\left(\frac{17}{36}-\frac{19}{45}\right)+...+\left(\frac{197}{4851}-\frac{199}{4950}\right)\)
Ta thấy :
\(\left(\frac{9}{10}-\frac{11}{15}\right)=\frac{1}{6}=\frac{1}{\left(2.3\right)}=\frac{1}{2}-\frac{1}{3}\)
\(\left(\frac{13}{21}-\frac{15}{28}\right)=\frac{1}{12}=\frac{1}{\left(3.4\right)}=\frac{1}{3}-\frac{1}{4}\)
\(\left(\frac{17}{36}-\frac{19}{45}\right)=\frac{1}{20}=\frac{1}{\left(4.5\right)}=\frac{1}{4}-\frac{1}{5}\)
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\(\left(\frac{197}{4851}-\frac{199}{4950}\right)=\frac{1}{2450}=\frac{1}{\left(49.50\right)}=\frac{1}{49}-\frac{1}{50}\)
\(\Rightarrow S=\frac{38}{25}+\left[\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{50}\right)\right]\)
\(\Rightarrow S=\frac{38}{25}+\left[\frac{1}{2}-\frac{1}{50}\right]\)
\(\Rightarrow S=\frac{38}{25}+\frac{24}{50}\)
\(\Rightarrow S=2\)
#~Will~be~Pens~#
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10/19-5/17+4/19-7/19-12/17+17/19
= (10/19+4/19+17/19)-(5/17+7/19+12/17)
= (10/19+4/19+17/19-7/19)-(5/17+12/17)
= (10/19+4/19+ 10/19)-17/17
= (10/19+10/19+4/19)- 1
= 24/19 - 1
= 1+5/19 - 1
= (1-1)+5/19
= 5/19.
Có bài toán lớp 5 nào ko hiểu cứ đăng lên mình giải cho, nhắn với mấy bạn cậu thế nhé.
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