lim n趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求
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limn趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求limn趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求limn趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求答案是e,主要
lim n趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求
lim n趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求
lim n趋于无穷(2n+3/2n+1)的n+1次方的极限怎么求
答案是e,
主要用公式lim(n → ∞) (1 + 1 / n)^n = e
=lim (1+ 1/(n +1/2) )^(n+1/2) * (1 + 1/(n +1/2))^1/2
左边有极限e,右边有极限1
故极限为e.
(2n+3/2n+1)^n+1
=((2n+1+2)/(2n+1))^(n+1)
=(1+2/(2n+1))^(n+1)
=(1+2/(2n+1))^(2n+1+1)/2
=e^1/2
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