n趋于无穷求(n+1)^1⼀3-n^1⼀3的极限

2024-11-25 20:21:24
推荐回答(2个)
回答1:

lim(n→∞) (n+1)^1/3-n^1/3 立方差公式,上下察销悉同时乘以 (n+1)^2/3+n^1/3*(n+1)^1/3+n^2/3
=lim(n→∞) [(n+1)-n]/败乎[(n+1)^2/3+n^1/3*(n+1)^1/3+n^2/斗迹3]
=lim(n→∞) 1/[(n+1)^2/3+n^1/3*(n+1)^1/3+n^2/3]
=0

回答2:

lim [(n+1)^(1/3) - n^(1/罩搏3)]
= lim [ (n/物升祥3 + 1/3) - n/笑改3 ]
= 1/3