问题 填空题
计算:
lim
n→∞
(1+
2
3n+1
)n
=______.
答案

3n+1
2
=t,则n=
2t-1
3

lim
n→∞
(1+
2
3n+1
)
n
=
lim
n→∞
(1+
1
t
)
2t-1
3
=
lim
n→∞
[(1+
1
t
)
t
] 
2
3
lim
n→∞
(1+
1
t
)
1
3
=e
2
3

故答案为:e

2
3

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