※ 引述《chiangpyisme (KK)》之銘言：
: 今天的考卷共有3題不會
: 跪求版上大大幫解題
: http://i.imgur.com/HKGPKAK.jpg
: 圖中多選題第六題選項四
: http://i.imgur.com/xoNvVSB.jpg
: 第E題
: http://i.imgur.com/gL0p9J6.jpg
: 第二題
1
(3) 原 = sum (k=1..n) ------------
(2k+1)(2k-1)
1 1
= sum (k=1..n) (1/2) [ ------- - -------]
2k-1 2k+1
= (1/2) [ ( 1/1 - 1/3 ) + ( 1/3 - 1/5 ) + ... ( 1/(2n-1) - 1/(2n+1)]
= (1/2) (2n)/(2n+1)
(1)
a_1 = 0 , d= -6
-6 -6 -6
原 = -------- + --------- + ... + ---------
3 * -6 4 * -12 11 * -54
1 1 1
= -------- + -------- + ... + ---------
3 * 1 4 * 2 11 * 9
1
= sum (k=2..10) -----------
(k+1) (k-1)
1 1
= sum (k=2..10) (1/2) [ ------ - ----- ]
k-1 k+1
= 36/55
(2) a_n = 3 * a_(n-1) + 1
=> a_n + k = 3 * [ a_(n-1) + k ] ( k = 1/2)
=> a_n + 1/2 = 3 * [ a_(n-1) + 1/2 ]
=> a_n + 1/2 = 3^(n-1) * ( a_1 + 1/2 ) = 3^(n-1) * 5/2
=> a_n = (5/2) * 3^(n-1) - 1/2
有錯還請不吝指正。
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※ 編輯: a016258 (140.114.137.240), 08/10/2017 17:12:27