作者Honor1984 (奈何上天造化弄人？)
看板Math
标题Re: [中学] AMC考题 1题
时间Wed Feb 3 02:54:46 2021
※ 引述《hero010188 (我是海贼王)》之铭言：
: https://i.imgur.com/I6Lxlvx.jpg
: 21 目前没想法中 >"<
x = 2^17
=> x - 1 = 1 + 2 + 2^2 + ... + 2^16
LHS = 1 - x + x^2 -... + x^16
= 1 + x(x - 1) + x^3(x - 1) + x^5(x - 1) + ... + x^15(x - 1)
8 16
= 2^0 + Sigma Sigma 2^[17(2k-1)+m]
k = 1 m = 0
=> a_k = 1 + 8 * 17 = 137
选(C)
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※ 编辑: Honor1984 (111.243.62.15 台湾), 02/03/2021 12:12:44
1F：推 adamchi : 谢谢您~ 02/03 15:02