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TA CÓ:\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
\(=\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{8}\)
\(=1-\frac{1}{8}=\frac{7}{8}\)
1=2:2+2-2
2=2:2+2:2
3=2*2-2:2
4=2*2*2:2
5=2*2+2:2
6=2*2*2-2
7=???????
8=2*2+2*2
9=???????
10=2*2*2+2
\(\frac{3}{2.3.4}+\frac{3}{3.4.5}+...+\frac{3}{100.101.102}\)
\(=\frac{3}{2}\left(\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{100.101}-\frac{1}{101.102}\right)\)
\(=\frac{3}{2}\left(\frac{1}{6}-\frac{1}{101.102}\right)\)