Question

 

A = 18 × ( 373737/424242 + 373737/565656 + 373737/727272)

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Answer 1

\(A=18\cdot\left(\frac{373737}{424242}+\frac{373737}{565656}+\frac{373737}{727272}\right)\)

\(=18\cdot\left(\frac{37}{42}+\frac{37}{56}+\frac{37}{72}\right)=18\cdot37\cdot\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)

\(=18\cdot37\cdot\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)\)

\(=18\cdot37\cdot\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=18\cdot37\cdot\left(\frac{1}{6}-\frac{1}{9}\right)=18\cdot37\cdot\left(\frac{3}{18}-\frac{2}{18}\right)\)

\(=18\cdot37\cdot\frac{1}{18}=18\cdot\frac{1}{18}\cdot37=1\cdot37=37\)