565656+585646
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\(\frac{575757}{424242}+\frac{575757}{565656}+\frac{575757}{727272}=\frac{57\times10101}{42\times10101}+\frac{57\times10101}{56\times10101}+\frac{57\times10101}{72\times10101}\)
\(=\frac{57}{42}+\frac{57}{56}+\frac{57}{72}=57\times\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)
\(=57\times\left(\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}\right)\)
\(=57\times\left(\frac{7-6}{6\times7}+\frac{8-7}{7\times8}+\frac{9-8}{8\times9}\right)\)
\(=57\times\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)
\(=57\times\left(\frac{1}{6}-\frac{1}{9}\right)=\frac{19}{6}\)
=\(70\left(\frac{121212}{565656}+\frac{121212}{727272}+\frac{121212}{909090}\right)\)
=\(70\left(\frac{3.40404}{14.40404}+\frac{121212}{6.121212}+\frac{2.60606}{15.60606}\right)\)
=\(70\left(\frac{3}{14}+\frac{1}{6}+\frac{2}{15}\right)\)
=\(70.\frac{18}{35}=38\)
http://coccoc.com/search#query=140.+(+505050%2F565656+%2B+505050%2F727272+%2B+505050%2F909090+)
\(140.\left(\frac{505050}{565656}+\frac{505050}{727272}+\frac{505050}{909090}\right)\)
\(=140.\left(\frac{50}{56}+\frac{50}{72}+\frac{50}{90}\right)\)
\(=140.\left(\frac{25}{28}+\frac{25}{36}+\frac{5}{9}\right)\)
\(=140.\frac{225+175+140}{252}\)
\(=140.\frac{540}{252}=140.\frac{15}{7}=300\)
1151302
\(565656+585646=1151302\)