6#
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小 發表於 2011-4-5 05:20 PM (第 4787 天)
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4. The limit doesn't exist
5,6 題是不是n→∞?
如果n→∞:
5. e-1/(1!) -2/(2!) -3/(3!) = e - 5/3
6. Let S be the answer.
-(3^4)S = -3^5/(5!) +3^6/(6!) -3^7/(7!) + ...
-(3^4)S = (-3)^5/(5!) +(-3)^6/(6!) +(-3)^7/(7!) + ...
-(3^4)S = e^(-3) - 1- (-3)^1/(1!) - (-3)^2/(2!) - (-3)^3/(3!) - (-3)^4/(4!)
-(3^4)S = e^(-3) - 11/8
S = [-e^(-3) + 11/8] / 81
都是用e^x = Sum[n=0 to ∞] (x^n)/(n!) 這條公式