Re: [中學] 16^x / (4+16^x)

※ 引述《mj813 (薩坨十二惡皆空)》之銘言： : 設 f(x)＝16^x / (4+16^x) : 求 f(1/6)+f(2/6)+f(3/6)+f(4/6)+f(5/6) : 拜託解惑，感激各位前輩！ 16^x = 2^4x f(x) = 2^4x/(4+2^4x) = 2^6x/(2^(2x+2)+2^6x) f(n/6) = 2^n/(2^(2+n/3)+2^n) n f(n/6) 1 2/(2^(2+1/3)+2)=1/[2^(4/3)+1] 2 4/[2^(2+2/3)+4]=1/[2^(2/3)+1] 3 8/[2^(2+1)+8]=1/2 4 16/[2^(2+4/3)+16]=1/[2^(-2/3)+1]=2^(2/3)/[1+2^(2/3)] 5 32/[2^(2+5/3)+32]=1/[2^(-4/3)+1]=2^(4/3)/[1+2^(4/3)] f(1/6)+f(5/6) = f(2/6)+f(4/6) = 1 Ans = 5/2 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 211.23.191.211 (臺灣) ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1728453710.A.322.html