lim[cos(x/2)(x/4)...(x/2~n)],n趋于无穷

题目详情

lim [cos(x/2)(x/4)...(x/2~n)],n趋于无穷

▼优质解答

答案和解析

(x/2)(x/4)...(x/2~n)]=x^n/2^[n(n+1)/2]
=[x/2^(n+1)/2]^n,当n趋向无穷大时lim[x/2^(n+1)/2]^n=0
lim [cos(x/2)(x/4)...(x/2~n)]=1

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