# 生活數學：地鐵新優惠計劃真的比較優惠？

$^Ad_n = 1$$n = 1,3,5...$
$^Ad_n = 0.9$$n = 2,4,6...$

$^Bd_n = 0.97$$n = 1,2,3...$

$\sum_{n=1}^{N}M_n d_n = M_1 \times d_1 + M_2 \times d_2 + M_3 \times d_3 + ... + M_N \times d_N$

$\sum_{n=1}^{N}M_n~^Ad_n - \sum_{n=1}^{N}M_n~^Bd_n > 0$

$\sum_{n=1}^{N}M_n (^Ad_n-~^Bd_n) > 0$

$\sum_{n=1,3,5...}M_n (1-0.97) + \sum_{n=2,4,6...}M_n (0.9-0.97) > 0$

$0.03\sum_{n=1,3,5...}M_n - 0.07\sum_{n=2,4,6...}M_n > 0$

$0.03\sum_{n=1,3,5...}M_n > 0.07\sum_{n=2,4,6...}M_n$

$\frac{\sum_{n=1,3,5...}M_n}{\sum_{n=2,4,6...}M_n} > \frac{0.07}{0.03} \approx 2.333$

## By David Yu

David Yu is the father of Simba and an Astrophysicist. He obtained his PhD in Astrophysics from the Max Planck Institute of Extraterrestrial Physics, Germany. He was formerly a postdoc at the KTH Royal Institute of Technology, Sweden, and is currently a lecturer at the University of Hong Kong. He served as the host of the RTHK TV31 programme Science Night, the Depute Editor-in-Chief of the Taiwanese Science Magazine Physics Bimonthly, and the Science Consultant of Stand News. The books he authored include Dr David’s 21 Mysteries of The Universe (2021), Space – A Down-to-Earth Astrophysicist (2021), Time – A Spacetime Journey of Astronomy and Physics (2019), and Secrets from the Stars (2017).