Question

[四种草药 - TFBoys]

Tính nhanh

210.(111111/121212 +111111/202020+11111/303030 + 111111/424242 +111111/565656 +111111/727272 +111111/909090)

Answer 1

[Vương Hải Nam]

Đặt 

\(A=210.\left(\frac{111111}{121212}+\frac{111111}{202020}+\frac{111111}{303030}+\frac{111111}{424242}+\frac{111111}{565656}+\frac{111111}{727272}+\frac{111111}{909090}\right)\)

     \(=210.\left(\frac{11}{12}+\frac{11}{20}+\frac{11}{30}+\frac{11}{42}+\frac{11}{56}+\frac{11}{72}+\frac{11}{90}\right)\)

    \(=210.11\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

     \(=2310.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

    \(=2310.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

     \(=2310.\left(\frac{1}{3}-\frac{1}{10}\right)\)

       \(=2310.\frac{7}{30}\)

        \(=539\)

Answer 2

[Phan Linh]

210.(111111/121212 +111111/202020+11111/303030 + 111111/424242 +111111/565656 +111111/727272 +111111/909090)

= 210 . ( 11/12+11/20+11/42+11/56+11/72+11/90)

= 210.(11.(1/12+1/20+1/42+1/56+1/72+1/90))

=210.(11(1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10))

=210.(11.(1/3-1/10))

=210.(11.7/30)

=210.77/30

=593

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