一年按365天算，单数日努力一点点，双数日颓废一点点，一年下来结果是多少？请写出高中数列公式解答。
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发布时间：2022-05-15 02:19
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热心网友
时间：2023-11-24 03:53
a(1)=1.01,a(2) = 0.99*1.01 = 0.9999.
a(2n+1) = (1+0.01)a(2n),
a(2n) = (1-0.01)a(2n-1).
a(2n+1) = (1+0.01)a(2n) = (1+0.01)(1-0.01)a(2n-1) = 0.9999a(2n-1),
{a(2n-1)}是首项为a(1)=1.01,公比为0.9999的等比数列。
a(2n-1) = 1.01 *(0.9999)^(n-1),
a(365) = a(2*183-1) = 1.01 *(0.9999)^(183-1) = 1.01* (0.9999)^(182)
=1.01 * (1.01*0.99)^(182)
=1.01 * [(1.01)^(364)(0.99)^(364)]^(1/2)
=1.01 *[(1.01)^(365)(0.99)^(365)]^(1/2) /[1.01*0.99]^(1/2)
=1.01 *[37.8 * 0.03]^(1/2) *[1.01*0.99]^(1/2) /[1.01*0.99]
= [37.8*0.03*0.9999]^(1/2)/0.99
= 1.0756
