Question

极限limn→∞1nnn(n+1)(n+2)…(2n?1)=______

极限limn→∞1nnn(n+1)(n+2)…(2n?1)=______．

Answer 1

由于

1

n

n	n(n+1)(n+2)…(2n?1)

=

1

n

n

k＝1

ln(1+

k

n

)
对已知式子求极限，

lim

n→∞

1

n

n	n(n+1)(n+2)…(2n?1)

=

lim

n→∞

1

n

n

k＝1

ln(1+

k

n

)
=

∫

1 0

ln(1+x)dx
=2ln2-1
=ln

4

e