Question

已知an=

.

2 n 1 n+1 1 n

.

，则

lim

n→∞

a_n=______．

Answer 1

∵an=

.

2 n 1 n+1 1 n

.

=

2

n

-

n

n+1

=

2n+2-n2

n2+n

，
∴

lim

n→∞

2n+2-n2

n2+n

=

lim

n→∞

2 n + 2 n2 -1

1+ 1 n

=-1．
故答案为：-1．