问题
选择题
若an是（1+x）n+1（n∈N*）展开式中含x2项的系数，则
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答案
∵a1=C22=1，a2=
=C 23
=3，a3=3×2 2×1
=C 24
=6，…，an=4×3 2×1
=C 2n+1
，(n+1)n 2×1
∴
（lim n→∞
+1 a1
+…+1 a2
）=1 an
(lim n→∞
+2 2×1
+2 3×2
+…+2 4×3
)2 (n+1)×n
=2
[(1-lim n→∞
)+(1 2
-1 2
)+(1 3
-1 3
)+…+(1 4
-1 n
)]1 n+1
=2
(1-lim n→∞
)1 n+1
=2lim n→∞ n n+1
=2．
故选A．