數學證明題！越簡短越好！

👨🏻‍🏫 學術台數學

2007-11-17 5:43 am

證明2+2^2+2^3+...+2^n<2^(n+1)

回答 (1)

2007-11-17 5:52 am

✔ 最佳答案

LHS = 2+2^2+2^3+...+2^n
=2[2^n - 1]/(2-1) [**Sum of geometric sequence]
= 2^(n+ 1) - 2
< 2^(n+1)

👍 0 👎 0

收錄日期: 2021-04-13 18:12:16
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071116000051KK03807

檢視 Wayback Machine 備份