5. 求s=1/2+2!/3+3!/4…(n-1)!/n直到最后一项大于1000

来源：百度知道 编辑：UC知道 时间：2024/06/24 14:39:26
请问如何用VB做
求s=1/2+2!/3+3!/4…(n-1)!/n直到最后一项大于1000
谢谢

证明：
当k=1时
1/2+1/3+1/4=13/12=26/24>25/24
结论成立。
假设k=n时结论成立，即
1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)>25/24
当k=n+1时
由于
9(n+1)^2=9n^2+18n+9>9n^2+18n+8=(3n+2)(3n+4)
即
9(n+1)^2/[(3n+2)(3n+4)]-1>0
左侧为
1/[(n+1)+1]+1/[(n+1)+2]+1/[(n+1)+3]+...+1/[3(n+1)+1]
=1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)+{1/(3n+2)+1/(3n+3)+1/(3n+4)-1/(n+1)}
=1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)+{6(n+1)/[(3n+2)(3n+4)]-2/(3n+3)}
=1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)+2/(3n+3)*{9(n+1)^2/[(3n+2)(3n+4)]-1}
>1/(n+1)+1/(n+2)+1/(n+3)+...+1/(3n+1)>25/24。
结论成立。

Dim s As Double
Dim i As Long
Dim b As Long
Dim l As Double
b = 1
i = 1
Sum = 0
Do
b = b * i
i = i + 1
l = b / i
s = s + l
Loop Until l > 1000