Question

[Nguyễn Võ Thanh Mai]

Tinh tong: 

13/3+13/6+13/10+13/15+13/21+13/28+13/36+13/45+13/55

Answer 1

[Phùng Minh Quân]

Đặt \(A=\frac{13}{3}+\frac{13}{6}+\frac{13}{10}+\frac{13}{15}+\frac{13}{21}+\frac{13}{28}+\frac{13}{36}+\frac{13}{45}+\frac{13}{55}\)

\(A=\frac{26}{6}+\frac{26}{12}+\frac{26}{20}+\frac{26}{30}+\frac{26}{42}+\frac{26}{56}+\frac{26}{72}+\frac{26}{90}+\frac{26}{110}\)

\(A=26\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\right)\)

\(A=26\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\right)\)

\(A=26\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(A=26\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(A=26.\frac{9}{22}\)

\(A=\frac{117}{11}\)

Vậy \(A=\frac{117}{11}\)

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