\(D=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)
\(D=\frac{5}{3}.\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)
\(D=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(D=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(D=\frac{5}{3}.\frac{1}{21}\)
\(\Rightarrow D=\frac{5}{63}\)
\(3D=3\left(\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+...+\frac{5}{123\cdot126}\right)\)
\(=\frac{3\cdot5}{18\cdot21}+...+\frac{3\cdot5}{123\cdot126}\)
\(=5\left(\frac{3}{18\cdot21}+...+\frac{3}{123\cdot126}\right)\)
\(=5\left(\frac{1}{18}-\frac{1}{21}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(=5\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(=5\left(\frac{7}{126}-\frac{1}{126}\right)\)
\(=5\cdot\frac{6}{126}\)
\(=\frac{30}{126}\)
\(D=\frac{30}{126}\div3=\frac{30}{126}\cdot\frac{1}{3}=\frac{5}{63}\)
\(#Cothanhkhe\)
Bạn trên làm sai rồi
D=5/18.21+5/21.24+…+5/123.126
D.3/5=3/5.(5/18.21+5/21.24+…+5/123.126
D.3/5=3/18.21+3/21.24+…+3/123.126
D.3/5=(1/18-1/21)+(1/21-1/24)+…+(1/123-1/126)
D.3/5=1/18-1/21+1/21-1/24+…+1/123-1/126
D.3/5=1/18-(1/21-1/21)+…+(1/123-1/123)-1/126
D.3/5=1/18+0+0+…+0-1/126
D.3/5=1/18-1/126
D.3/5=7/126-1/126
D.3/5=5/126
D=5/126:3/5
D=5/126.5/3
D=25/378
Vậy D=25/378
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