B=5/2x7+5/4x9+...+5/48x53
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\(=5+\dfrac{4}{5}\left(\dfrac{5}{2\cdot7}+\dfrac{5}{7\cdot12}+...+\dfrac{5}{52\cdot57}\right)\)
\(=5+\dfrac{4}{5}\left(\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+...+\dfrac{1}{52}-\dfrac{1}{57}\right)\)
\(=5+\dfrac{4}{5}\cdot\dfrac{55}{114}=\dfrac{307}{57}\)
\(\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{54.59}=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{54}-\frac{1}{59}=\frac{1}{4}-\frac{1}{59}=\frac{55}{236}\)
\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}\)
\(=12:\left\{400:200\right\}\)
=12:2
=6
\(\left(\frac{13}{84}.\frac{7}{5}-\frac{5}{2}.\frac{7}{180}\right):\frac{43}{18}+\frac{9}{2}.\frac{1}{10}\)
\(=\frac{43}{360}:\frac{43}{18}+\frac{9}{20}=\frac{1}{20}+\frac{9}{20}=\frac{10}{20}=\frac{1}{2}\)