问题 解答题
求下列极限:
(1)
lim
n→∞
2
n
+n+7
5n2+7

(2)
lim
n→∞
n2+n
-n);
(3)
lim
n→∞
2
n2
+
4
n
+…+
2n
n2
).
答案

(1)

lim
n→∞
2n2+n+7
5n2+7
=
lim
n→∞
2+
1
n
+
7
n2
5+
7
n
=
2
5

(2)

lim
n→∞
n2+n
-n)=
lim
n→∞
n
n2+n
+n
=
lim
n→∞
1
1+
1
n
+1
=
1
2

(3)原式=

lim
n→∞
2+4+6++2n
n2
=
lim
n→∞
n(n+1)
n2
=
lim
n→∞
(1+
1
n
)=1.

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