Question

[Lê Mai Liên]

tính nhanh

121212 / 151515 + 121212 / 353535 + 121212 / 636363 + 121212 / 999999

Answer 1

[Nguyễn Đình Dũng]

\(\frac{121212}{151515}+\frac{121212}{353535}+\frac{121212}{636363}+\frac{121212}{999999}\)

= \(\frac{12.10101}{15.10101}+\frac{12.10101}{35.10101}+\frac{12.10101}{63.10101}+\frac{12.10101}{99.10101}\)

= \(\frac{12}{15}+\frac{12}{35}+\frac{12}{63}+\frac{12}{99}\)

= \(\frac{12}{3.5}+\frac{12}{5.7}+\frac{12}{7.9}+\frac{12}{9.11}\)

= \(6.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

= \(6.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

= \(6.\left(\frac{1}{3}-\frac{1}{11}\right)\)

= \(6.\frac{8}{33}\)

= \(\frac{16}{11}\)