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\(\frac{15.\left(\frac{1}{616}.\frac{1}{6.16}.\frac{1}{6.16}\right)}{33.\left(\frac{1}{6.16}.\frac{1}{6.16}.\frac{1}{6.16}\right)}=\frac{15}{35}\)
a,A=\(\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+.........+\frac{1}{23.24}\)
A=\(\frac{1}{2}+\frac{2}{1}-\frac{1}{3}+\frac{3}{1}-\frac{1}{4}+......\frac{23}{1}-\frac{1}{24}\)
A=\(\frac{1}{2}-\frac{1}{24}\)
A=\(\frac{11}{24}\)
\(A=\frac{\frac{3}{2}\left(\frac{1}{6}-\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}\right)}{\frac{33}{10}\left(\frac{1}{6}-\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}\right)}=\frac{\frac{3}{2}}{\frac{33}{10}}=\frac{3}{2}:\frac{33}{10}=\frac{5}{11}\)
\(B=\frac{1}{16}+\frac{6}{16.26}+\frac{6}{26.36}+...+\frac{6}{2006.2016}\)
\(B=\frac{1}{16}+6\left(\frac{1}{16.26}+\frac{6}{26.36}+...+\frac{6}{2006.2016}\right)\)
\(B=\frac{1}{16}+\frac{6}{10}\left(\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}+...+\frac{1}{2006}-\frac{1}{2016}\right)\)
\(B=\frac{1}{16}+\frac{6}{10}\left(\frac{1}{16}-\frac{1}{2016}\right)\)
\(B=\frac{1}{16}+\frac{6}{10}.\frac{125}{2016}\)
\(B=\frac{1}{16}+\frac{25}{672}\)
\(B=\frac{67}{672}\)