问题
填空题
计算
|
答案
∵2[
+1 1×3
+…+1 2×4
]1 n(n+2)
=1-
+1 3
-1 2
+…+1 4
-1 n 1 n+2
=1+
-1 2
-1 n+1
=1 n+2
-3 2 2n+3 (n+1)(n+2)
∴
+1 1×3
+…+1 2×4
=1 n(n+2)
-3 4 2n+3 2(n+1)(n+2)
∴
[lim n→∞
+1 1×3
+…+1 2×4
]=1 n(n+2)
[lim n→∞
-3 4
]=2n+3 2(n+1)(n+2) 3 4
故答案为：3 4