Re: [中學] 高中一題數列與級數問題

[Honor1984 (奈何上天造化弄人？)]

※ 引述《yizihappyQ (Ms.Q)》之銘言：
: 請問這題要怎麼解？謝謝
: https://i.imgur.com/I0xzPTa.jpg

[(a_n + 2)/2]^2 = 2S_n

8S_n = (a_n + 2)^2

8a_1 = (a_1 + 2)^2 => a_1 = 2

8a_n = (a_n + 2)^2 - [a_(n-1) + 2]^2

=> (a_n - 2)^2 = [a_(n-1) + 2]^2

由題設知

=> a_n = a_(n-1) + 4

=> a_2015 = 2 + 4 * 2014 = 8058


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