利用夹逼定理,求数列极限 lim(1+2∧n+3∧n)∧1╱n

2024-11-13 04:07:20
推荐回答(1个)
回答1:

极限 = 3
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解析:
A = lim(3^n)^(1/n) = 3
B = lim(1+2^n+3^n)^(1/n)
C = lim(3^n+3^n+3^n)^(1/n) = lim 3^[(n+1)/n] = 3

因为 A ≤ B ≤ C,且 A = C = 3,
所以 B = 3