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Giải chi tiết hộ mình với ạ

DL
21 tháng 7 2022 lúc 16:10

\(N=\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{73.76}\\ \rightarrow N=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{73}-\dfrac{1}{76}\\ N=\dfrac{1}{4}-\dfrac{1}{76}\\ N=\dfrac{9}{38}\)

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\(I=\dfrac{12}{4.7}+\dfrac{12}{7.10}+...+\dfrac{12}{73.76}\\ \rightarrow\dfrac{1}{4}.I=\dfrac{1}{4}.\left(\dfrac{12}{4.7}+\dfrac{12}{7.10}+...+\dfrac{12}{73.76}\right)\\ \dfrac{1}{4}.I=\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{73.76}\\ \dfrac{1}{4}.I=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{73}-\dfrac{1}{76}\\ \dfrac{1}{4}.I=\dfrac{1}{4}-\dfrac{1}{76}=\dfrac{9}{38}\\ I=\dfrac{9}{38}:\dfrac{1}{4}\\ I=\dfrac{18}{19}\)

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\(K=\dfrac{5}{4.7}+\dfrac{5}{7.10}+...+\dfrac{5}{73.76}\\ \rightarrow\dfrac{3}{5}K=\dfrac{3}{5}\left(\dfrac{5}{4.7}+\dfrac{5}{7.10}+...+\dfrac{5}{73.76}\right)\\ \dfrac{3}{5}K=\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{73.76}\\ \dfrac{3}{5}K=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{73}-\dfrac{1}{76}\\ \dfrac{3}{5}K=\dfrac{1}{4}-\dfrac{1}{76}=\dfrac{9}{38}\\ K=\dfrac{9}{38}:\dfrac{3}{5}\\ K=\dfrac{15}{38}\)

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\(L=\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{73.76}\\ \rightarrow3L=3\left(\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{73.76}\right)\\3L=\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{73.76}\\ 3L=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{73}-\dfrac{1}{76}\\ 3L=\dfrac{1}{4}-\dfrac{1}{76}=\dfrac{9}{38}\\ L=\dfrac{9}{38}:3\\ L=\dfrac{3}{38}\)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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