根值判别法 ∑(cos1/n)^n^3

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根值判别法 ∑(cos1/n)^n^3

lim[(cos1/n)^n^3]^(1/n)
=lim(cos1/n)^(n^2)
=lim(1+cos1/n-1)^(n^2)
=lim[(1+cos1/n-1)^(1/(cos1/n-1))]^ [(n^2)((cos1/n-1)]
lim[(1+cos1/n-1)^(1/(cos1/n-1))]=e
lim[(n^2)((cos1/n-1)]=limn^2(-1/(2n^2))=-1/2
极限=e^(-1/2)