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\(14.\frac{5}{21}=\frac{14}{1}.\frac{5}{21}=\frac{14.5}{21}=\frac{10}{3}\)
\(\frac{5}{21}.14=\frac{5.14}{21.1}=\frac{5.2}{3.1}=\frac{10}{3}\)
\(10:\frac{5}{3}=10.\frac{3}{5}=\frac{10.3}{5}=2.3=6\)
\(\frac{5}{3}:10=\frac{5}{3}.\frac{1}{10}=\frac{5}{3.10}=\frac{1}{6}\)
\(8:\frac{4}{5}-7\frac{1}{5}\times\frac{5}{4}=8\times\frac{5}{4}-\frac{36}{5}\times\frac{5}{4}\)
\(=\frac{5}{4}\times\left(8-\frac{36}{5}\right)\)
\(=\frac{5}{4}\times\frac{4}{5}\)
\(=1\)
\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)
=\(\frac{3}{1.2}+\frac{3}{2.4}+\frac{3}{4.8}+\frac{3}{8.16}+\frac{3}{16.32}\)
=\(\frac{3}{1}-\frac{3}{2}+\frac{3}{2}-\frac{3}{4}+\frac{3}{4}-\frac{3}{8}+\frac{3}{8}-\frac{3}{16}+\frac{3}{16}-\frac{3}{36}\)
=\(\frac{3}{1}-\frac{3}{36}\)=\(\frac{35}{12}\)
\(\frac{1}{5}\cdot\frac{1}{7}+\frac{4}{5}+\frac{1}{5}\cdot\frac{12}{7}-1-\frac{1}{5}\cdot\frac{6}{7}\)
\(=\frac{1}{5}\cdot\left(\frac{1}{7}+\frac{12}{7}-\frac{6}{7}\right)-\left(1-\frac{4}{5}\right)\)
\(=\frac{1}{5}.1-\frac{1}{5}\)
\(=\frac{1}{5}-\frac{1}{5}=0\)
1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200