Re: [高中] 數列
設b(n+1) = 1/a(a+1) = 1+3b(n), b(1) = 3
則b(n+1)+1/2 = 3/2+3b(n) = 3(1/2+3b(n))
b(2)+1/2 = 3(1/2+b(1))
b(3)+1/2 = 3(1/2+b(2))
......................
X)b(n)+1/2 = 3(1/2+b(n-1))
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約掉得
b(n)+1/2 = 3^n-1(1/2+3) = 3^n-1*7/2
b(n) = 3^(n-1)*7/2-1/2
a(n) = 2/7*3^(n-1)-1 #
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03/04 01:05, , 1F
03/04 01:05, 1F
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